How to Record Your Twitch Broadcasts for Later Review

Take advantage of Twitch’s Videos On Demand (VOD) system and automatically archive broadcasts

By default, Twitch doesn’t save your previous broadcasts. To enable automatic archiving of broadcasts:

  1. Visit your “Channel & Videos” tab
  2. Tick the checkbox next to Archive Broadcasts

Twitch will retain your past broadcasts at https://www.twitch.tv/USERNAME/videos/past-broadcasts

Regular broadcasters will have their broadcasts saved for two weeks, while Turbo subscribers (Twitch Prime included!) and Partners enjoy 60-day storage. During this time you can create highlights from your broadcasts and export your VODs directly to YouTube by visiting the Video Manager at https://www.twitch.tv/USERNAME/manager/

and/or record locally

Beware that working with video is resource-intensive.

Sources
https://help.twitch.tv/customer/portal/articles/1575302-videos-on-demand