I would like to record or replay my games.

Seriously shocked Riot hasn't build in replays yet. DOTA had replays more than a decade ago

The most common thing for this is lolreplay, I have heard it works really well for most people but some do have issues with it.

I went from lolreplay to Baronreplays. No real difference, but both sometimes have problems that prevent you from watching a replay it recorded so I'd suggest having both so you can switch when your favored one has an issue.

op.gg

After u start ur game, go to na.op.gg and search for your profile Below "RENEW DATA", click "INGAME INFO", then there's a button to record, sometimes it's not working but I don't know why since it's in Korean.

my fav, no downloads needed.