(covers information from an alternate timeline)
Early career Edit
Prior to being assigned to Earth, Soval was part of negotiations regarding the last accord between the Vulcans and the Andorians prior to 2152. During the work on the project, Shran gained a respect for him. (ENT: "Kir'Shara")
Soval was one of the greatest proponents of cautioning Earth's advancement into the galaxy. Jonathan Archer blamed Soval for holding back the warp five engine's development so much that his father, Henry Archer, died before his design became a reality.
After Klingon courier Klaang crash-landed on Earth in 2151, Soval – along with two senior aides of his, T'Pol and Tos – recommended that Enterprise's launch be postponed, due to possible diplomatic repercussions involving Klaang. At Starfleet Medical, Soval also recommended taking the Klingon off life support and returning his corpse to Qo'noS; Admiral Maxwell Forrest ignored this recommendation, and decided this was a perfect opportunity to launch Enterprise. Soval offered the ship's crew use of the Vulcan database, under the condition that Enterprise take T'Pol along as a science officer. (ENT: "Broken Bow")
When the Vulcans monitored Enterprise docking with a v'tosh ka'tur vessel, the Vahklas, Soval was asked to pass on a message from a Vulcan High Command minister to Admiral Forrest, who passed it on to Captain Archer. The message was that Kov's father was dying and wished to contact him. (ENT: "Fusion")
Six months later, Soval informed Admiral Forrest that – due to Captain Archer having interfered at P'Jem, which had led to it subsequently being destroyed by the Andorians – Earth and Vulcan's joint fleet operations would be suspended. Soval was also recalled to Vulcan for consultation. (ENT: "Shadows of P'Jem")
In 2152, after Enterprise was incorrectly deemed responsible for destroying the Paraagan colony, Soval recommended that Earth cease its deep-space exploration efforts for the next decade or two. However, Starfleet Command ignored this recommendation, as well, when it was discovered that a third party had sabotaged and framed Enterprise for the colony's destruction. (ENT: "Shockwave, Part II")
Later that year, when fighting once again broke out on the disputed planet Paan Mokar between Vulcan and Andorian forces, Shran asked the Vulcans to send "Archer" to help in the peace talks, as he was someone they trusted. The Vulcan High Command had Soval (as ambassador to Earth) contact Starfleet and Captain Archer. Soval and Sub-Commander Muroc met with Enterprise to relay the message. Soval was not particularly pleased to have Archer there, and was suspicious of why an Andorian would ask for him. But after some negotiating with Archer, he agreed to go down to the planet with him to meet with Shran (citing "the ball is in our court now," a Human phrase).
While attempting to land on Paan Mokar in a shuttle, the vehicle was shot down by renegade members of the Andorian forces, not working under Shran's orders. Although Soval suggested meeting up with the Vulcan forces, Archer insisted on heading towards Shran. Soon, they came under fire, and Soval was shot in the shoulder by an Andorian. T'Pol helped put his arm in a sling, and they sought cover. When Archer went to come up on the attackers from behind, he handed a phase-pistol to Soval and told him to give him cover. Soval, not having fired a weapon since the 2100s, was wary about it, but did so. Shortly after one of the Andorians firing on them was taken out, Soval and T'Pol were captured by the Andorian forces and taken to Shran, who had found Archer fighting with one of the renegade Andorians. Once the renegade Andorian, Tarah, was arrested, real peace talks began between Shran, Soval, T'Pol, Muroc and Archer, on Enterprise. Although they agreed that they didn't agree on much, they did settle that the talks would continue on Andoria. To celebrate, Shran insisted that they drink to it with Andorian ale. Although reluctant, Soval did not wish to offend Shran, and partook in the gesture. As T'Pol escorted the ambassador to the Vulcan ship, he pointed out to Captain Archer, regarding the situation, "Your presence here has not been... overly meddlesome." (ENT: "Cease Fire")
In 2153, Soval expressed skepticism regarding information Archer had gained from the Suliban about the Xindi and recommended against Enterprise undertaking a mission into the Delphic Expanse. He also tried to stop Sub-Commander T'Pol from joining the ship on its mission, once it became apparent that Captain Archer would not listen to him. (ENT: "The Expanse")
Upon Enterprise returning to Earth in 2154, Soval was on a board that investigated Captain Archer's mission in the Delphic Expanse. Soval reprimanded him for several concerns regarding the Vulcan ship Seleya, which Enterprise had encountered in the Expanse. One of Soval's many complaints was that Archer hadn't retrieved the ship's data recorder, so that the panel could truly know what had happened aboard the ship. However, Soval thanked Archer for saving their region of the galaxy from the Sphere-Builders, as information T'Pol reported showed their space would have eventually consumed many more worlds, including Vulcan. (ENT: "Home")
Later that year, Soval and Admiral Forrest were on Vulcan, discussing future relations between their two peoples. Soval was nearly killed when the United Earth Embassy on Vulcan was bombed; only Admiral Forrest taking action quickly saved Soval's life, at the cost of the admiral's own. Suspicious of the High Command claiming Syrrannite involvement in the bombing, Soval encouraged Captain Archer to pursue their own investigation and gave the captain his full support. Soval actively assisted Captain Archer and T'Pol in their mission to the Forge by providing them with information on the blind spots in the Vulcan Security Network so they transport in unnoticed. Soval later disclosed his ability as a mind-melder when he melded with a comatose embassy guard, Corporal Askwith, in order to find out the identity of the bomber, later revealed to be Stel – the chief investigator of the Vulcan Security Directorate. (ENT: "The Forge"). The meld, considered deviant in Vulcan society, prompted the High Command to strip Soval of his position as ambassador to Earth. (ENT: "Awakening")
After being dismissed from that role, he actively assisted Commander Tucker, who was commanding Enterprise in Captain Archer's absence, to uncover events that were unfolding. (ENT: "Awakening", "Kir'Shara") During these events, Soval essentially took over T'Pol's role as science officer, even working at her station on the bridge. (citation needed • edit)
Soval then informed Commander Tucker of a plot, orchestrated by High Command Administrator V'Las, to use the Syrrannite crisis as a cover for a planned invasion of Andoria, despite a peace treaty signed two years previously. Since such an action could have led to interstellar conflict, Soval decided to warn the Andorians of the impending invasion. A skeptical Commander Shran, unable to believe that the distinguished ambassador would so easily betray his own government, kidnapped Soval from Enterprise and subjected him to mental torture that lowered his emotional threshold in order to confirm his story. Soval's insistence and a few warning shots from Enterprise persuaded Shran to return Soval and advise the Andorian Imperial Guard of Vulcan movements based on Soval's data. (ENT: "Awakening")
With the element of surprise gone, the Vulcan invasion force met stiff resistance from the Andorians and Enterprise, giving enough time for the Kir'Shara to reach the Vulcan capital from Vulcan's Forge. Upon the activation of the Kir'Shara's writings, Administrator V'Las was relieved of his post and the invasion stopped by Minister Kuvak. Soval later informed Captain Archer of the dissolution of the High Command and the less stringent policy to be adopted towards Earth. (ENT: "Kir'Shara")
Following T'Pau's ascension to administrator, Soval was reinstated as the Vulcan Ambassador to Earth. He was one of several Vulcan ambassadors who represented their people at an historic conference to discuss the formation of a "Coalition of Planets". He was the first ambassador to give a standing ovation to a speech delivered by Captain Archer and Nathan Samuels. (ENT: "Terra Prime")
Despite his attempts to constrain Starfleet's warp development, Soval later admitted that he had gained a respect for Earth and its people during his years on the planet. When Tucker sarcastically remarked that he'd done a very good job at hiding it, Soval took that as a compliment. (ENT: "Awakening")
Alternate timelines Edit
"Listen to me, you're making a mistake!"
"When your logic doesn't work, you raise your voice? You've been on Earth too long."
"They've been in space for six months and they've already destabilized an entire sector."
"What is their fixation with our ears?"
"I believe they're envious."
"Join me in a drink to celebrate our mutual dissatisfaction."
"Vulcans don't drink... but this occasion merits an exception."
"Captain, your presence here has not been... overly meddlesome."
"Our Science Directorate has determined that time travel is impossible."
"Ambassador... I want to apologize for what I said to you the other day. I was out of line."
"Yes, you were."
"I'm glad we can finally agree on something."
"Captain... your actions, while being morally questionable, were necessary. I opposed your appointment as captain of Enterprise, but it's obvious now that I was wrong. T'Pol has told me that the Expanse would have someday encompassed hundreds of systems, including Vulcan. You've done a great service for both our worlds. Thank you."
"We don't know what to do about Humans. Of all the species we've made contact with, yours is the only one we can't define. You have the arrogance of Andorians, the stubborn pride of Tellarites. One moment you're as driven by your emotions as Klingons, and the next you confound us by suddenly embracing logic!"
"I'm sure those qualities are found in every species."
"Not in such confusing abundance."
"Ambassador... are Vulcans afraid of Humans?"
- (Soval answers with a slight nod)
"Because, there is one species you remind us of."
"There are those on the High Command who wonder what Humans would achieve in the century to come, and they don't like the answer."
"We're not the Klingons. We only want to be your partners, to do what the nations of Earth have learned to do: to work together in common cause."
"Your accomplishments have been noteworthy."
"They don't justify deception..."
"Deception has never been a stranger to this room."
"There's a great deal that needs to be said, Excellency, but no one's willing to listen."
"Mind if I ask you something? Why are you doing this? I never got the impression that you cared that much about Humans. Seems like... you were always finding something new to complain about."
"I lived on Earth for more than 30 years, Commander. In that time I developed an affinity for your world and its people."
"You did a pretty good job of hiding it."
"How many warning shots do Vulcans usually fire?"
- - Commander Tucker and Ambassador Soval after the Vulcan ships fired a shot that missed Enterprise by just 20 meters. (ENT: "Awakening")
"I'LL TEAR THE ANTENNAE FROM YOUR SKULL!!"
"Open a channel."
"Where is your fleet?!"
"Do you know the story of Nirak?"
"He was a soldier who lived a long time ago. He was standing watch over the gates of the city of Gol and he saw a cloud on the horizon moving toward him. He thought it was a sandstorm, so he told no one. It was an army. They destroyed the city, but they let Nirak live. His name now means "fool" in our language, just as yours will in Andorian!"
"How do you feel, captain?"
"Like a giant weight's been lifted"
Background information Edit
While Rick Berman and Brannon Braga were developing Star Trek: Enterprise pilot episode "Broken Bow", they had no idea that Soval would become a long-term recurring character. ("Broken Bow" audio commentary, ENT Season 1 DVD/Blu-ray) Consequently, in a character breakdown sheet that Paramount sent to various talent agents upon casting "Broken Bow", Ambassador Soval was said to be a non-recurring role. The character was, in the same document, further detailed thus; "Vulcan male. Late 60s. A wise and arrogant diplomat who has very little patience with Captain Archer." 
In 2014, it was announced Graham would reprise the role of Soval in the fan-made production Star Trek: Axanar.