Yes you can record meetings in Teams by clicking the record button at any time during the meeting. On the meeting toolbar, click the three dots:
Then click Start Recording button:
All recordings are uploaded to Microsoft Stream which everyone has access to with their office 365 account. Whoever starts the recording, it will be uploaded to their account. Once uploaded to Stream and ready, the user will be notified. From Stream the recording can be shared out easily.
To access Microsoft Stream, simply log into https://office.com with your email address and password, then click on the Stream tile:
Every recording is transcribed and that transcription is searchable. So if you search for a specific word, it will show you every time that word was spoken during the recording and if you click an entry, it will take you right to the point in the recording where it was spoken.