The following can be downloaded using your podcast app of choice. Some choose to use the 'Overcast' app as it's a better interface.
Film
The Business with Kim Masters
The Town with Matt Beloni
The Directors Cut—The Directors Guild of America
The FilmUp Podcast
TV's Top 5—Hollywood Reporter
Fresh Air—NPR
On with Kara Swisher
Theater
Stages Podcast—hosted by Stephanie J. Block and Marylee Fairbanks
American Theatre's Off Script
Three on the Aisle—hosted by American Theatre Magazine
The Theatre Podcast with Alan Seales
The American Theatre Wing has a whole host of podcasts: Downstage Center, Working in the Theatre, SDCF Masters of the Stage, Guide to Careers in the Theatre, This is Broadway, and possibly more
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