3 answers
Italicized formatting often varies depending on where it is being written. However, in typical written English, titles of larger works, which include books, albums, movies, and yes, podcasts, are usually italicized. So, 'The Daily', a popular podcast, should be written in italics. But always double-check for any specific formatting requirements in your scenario.
Whether to italicize podcasts or not can sometimes spark a debate, but as someone who has been involved in writing and editing, here's my two cents. Typically, English style guidelines such as those presented by APA, MLA, and Chicago Manual of Style all suggest the same thing: that titles of complete works should be italicized. This includes books, films, albums, and podcasts.
So, for example, if you were to mention the podcast 'Serial', it would be appropriate to italicize the name. However, the names of specific episodes should be quoted, not italicized.
The general rule of thumb is that the titles of full-length works should be italicized. This includes books, movies, albums, etc., and yes, even podcasts. For example, if you're referring to the podcast 'StartUp', you should italicize the title.
On the other hand, smaller works like articles, songs, and podcast episodes should be in quotation marks. So, yes, as a quick answer, podcasts are usually italicized when written in text. But, as always, different institutions or publications may have their own specific formatting rules, so make sure to check those out!