Wade is the son of former NFL coach Bum Phillips and Helen Wilson Phillips. He adored his father, both personally and professionally, stating, “I was blessed to have him as a father and coach. I got to coach with him for 11 years. He taught me everything I know about coaching. He taught me right and wrong. He taught me to enjoy life.”  Wade and wife Laurie met in 1964 at Port Neches–Groves High School, where he was the quarterback of the football team and she was the head cheerleader; they have a daughter, Tracy, an actress, dancer and choreographer living in Southern California, and a son, Wes, who is the tight ends coach for the Washington Redskins.
Wade has said this on his personal drive: "Winning is why we play and coach—our team and our fans is why we continue that quest."
Phillips began his professional coaching career in Houston as the linebackers coach in 1976 for the team coached by his father, as well as defensive line coach in 1977–1980. He remained on his father's staff as the pair headed for New Orleans. Bum stepped down as head coach of a struggling Saints team in late 1985, and Wade stepped in as interim head coach. He spent the next three years as the defensive coordinator of the Philadelphia Eagles and then four more in the same position for the Denver Broncos. Phillips replaced Dan Reeves as head coach for the Broncos in 1993, but was fired after a mediocre 1994 season in which management felt he lost control of the team.
Prior to the 2009 season, Phillips also took over as defensive coordinator, replacing the fired Brian Stewart. Phillips called defensive plays for the final 10 games of the 2008 season after Stewart was stripped of the responsibilities. In the 2009-10 playoffs, Phillips's Cowboys defeated the Eagles in the wild card round, ending the club's 12 year playoff win drought (6 games total, Phillips was only coach for one of those losses) and earning Phillips his first playoff win. Following the 2009 season, Phillips signed a contract extension through the 2011 season. However, he was fired by the Cowboys on 8 November 2010 following the second worst start in franchise history (one win in their first eight games) punctuated by a 45–7 loss to the Green Bay Packers.
Prior to the 2011 season, Phillips was hired as the defensive coordinator of the Houston Texans replacing Frank Bush, who was released by Texans owner Bob McNair. The Texans defense made major improvements on defense in Phillips's first year calling Houston's defense. Houston allowed the fourth-fewest points in the league in 2011 (compared to fourth most in 2010), the second-fewest yards allowed (third-most in 2010) and third-fewest yards per play (4.8, compared to 6.0, second-worst in 2010). On 3 November 2013, Texans Head Coach Gary Kubiak collapsed at the end of the first half of the Texans-Colts game, he was then hospitalized at a local hospital. In Kubiak's absence, Phillips was given the head coaching duties as the acting head coach for the remainder of the game. On 6 November 2013, the Texans, and Kubiak decided to temporarily hand Phillips the head coaching duties, and named him the interim head coach until Kubiak was medically cleared to return. Exactly one month later, Kubiak was fired after his team had lost 11 games in a row. Once again, Phillips served as interim head coach for the Texans until the end of the season, when former Penn State head coach and New England Patriots offensive coordinator Bill O'Brien was hired as the new head coach.