Mike Dombrowski has set up a webservice called AudioDidact.
There you can enter a YouTube URL and the service will download the audio content of the video (optionally event the whole video), and provide it as a public or private audio podcast, which you can then stream or download via your smartphone (e.g. with AntennaPod).
The webservice is open source and can be downloaded from GitHub and selfhosted, if you prefer this option.