It has been reported that Jakob does not like his famous father to be mentioned during interviews. This is not because of animosity between the two, as is widely assumed, but because Jakob has stated that he wants to make his own name for himself, and does not want to open doors or sell tickets by capitalizing on his family name.

The Wallflowers started out playing alongside other aspiring rockers at Canter's delicatessen in the Fairfax District of Los Angeles. The band signed to Virgin Records and made a self-entitled album, the cover of which had a picture of all the band members' feet, and drummer Peter Yanowitz' dog.

The debut sold poorly, however, and after they were released from Virgin Records, the band regrouped. They toured with 10,000 Maniacs, Toad The Wet Sprocket, Cracker, and The Spin Doctors, and gained and lost several band members along the way. With the help of their manager Andrew Slater, the band secured a new major label record deal with Interscope Records.

Their 1996 album Bringing Down the Horse, recorded with producer T-Bone Burnett (and including collaborations with Michael Penn, Adam Duritz, Mike Campbell, Don Heffington of Lone Justice, and Sam Phillips), yielded several singles, including "Sixth Avenue Heartache" and "One Headlight." The album sold over four million copies, and The Wallflowers won two Grammy Awards, for Best Rock Vocal Performance by a Duo or Group and Best Rock Song. "One Headlight" also won the VH-1 Video of the Year for 1997.

Jakob shares his family's desire for an anonymous personal life: "The world's as big as the block you live on, and I like to keep it small. I have had the same friends since I was eleven years old." Jakob says he is often amused when asked the question, "When did you change your name to Dylan?"

Jakob married his childhood sweetheart, Nicole Paige Denny (now actress Paige Dylan), in a ceremony at Sara Dylan's house in 1992. Their first child, Levi, was born two years later. They had a second son James in 1998 and a third son in 2000.