Vogel first auditioned for the Jim Henson Company in 1993 and joined the crew of Sesame Street in 1996 as an ensemble puppeteer. He has served as a director and puppet captain on Sesame Street since 2008. He inherited many of Jerry Nelson's Muppet character roles in 2008, when he began performing with The Muppets Studio. Since 2017, he has been the performer of Kermit the Frog.
With the Muppets, Vogel is one of the principal cast performers with the roles of Kermit, Floyd Pepper, Uncle Deadly, Lew Zealand, Crazy Harry, Robin the Frog, Sweetums, Camilla the Chicken, and Constantine under his tutelage. On Sesame Street, Vogel is the performer of Count von Count, and Big Bird. On Oobi, he performed Angus.
Beginning his puppeteering career at the Jim Henson Company in the 1990s, Vogel later served as the assistant puppeteer for Ernie on Sesame Street, performing with Steve Whitmire. After studying the role of Big Bird under the performance of Caroll Spinney from 1996, he inherited the role, explaining "It takes a lot of physical exertion" and "I'm wearing the body of the bird". Spinney remarked that "Vogel" is the German translation for "bird". He also took over the puppetry of the Sesame Street character Count von Count, and also the voice after Jerry Nelson died in 2012.
With The Muppets Studio, Vogel has been performing since 2008, and has appeared in The Muppets, Muppets Most Wanted, and a short-lived primetime series. Vogel performed the Muppets that were used in Kenneth's view of the world in the 30 Rock episode "Apollo, Apollo". In 2016, Vogel voiced the character of Wilkins in Alice Through the Looking Glass directed by James Bobin.
From 2017 onward, Vogel was cast as the new performer for Kermit the Frog, replacing Steve Whitmire. His first official performance as Kermit was scheduled to take place during a "Muppets Thought of the Week" segment to be uploaded on the Muppets' official YouTube channel. The video was uploaded in August 2017.