Podcasts can be searched on the iPhone via iTunes, on Android devices in the Google Play Store with the keyword Podcast. In addition to the internal search in the apps, special websites make it possible to listen to and record podcasts. In German https://www.phonostar.de/, in English http://www.podcasts.com/, https://www.mixcloud.com/, https://audioboom.com/, https://www.acast.com .

Special search engines make it possible to search in the content itself by converting the spoken language into text: https://www.listennotes.com/, https://fluiddata.com, https://www.spaactor.com/ (German)
or the metadata can be read out (all German search engines):
https://fyyd.de/, https://panoptikum.io/, https://wissenschaftspodcasts.de/, https://www.podcast.de