How do I block someone on Gmail so their emails stop reaching my inbox?

Open any email from them, click the three-dot menu at the top-right of that email, and choose 'Block [sender]'. From then on their emails skip your inbox and go straight to Spam. Blocking vs spam: blocking auto-routes that specific sender to Spam every time; 'Report spam' also tells Google the message is junk, which trains the filter and can hurt the sender's reputation. For someone persistent, use both. Manage or unblock later under Settings > Filters and Blocked Addresses. Note it's per address, if they email from a new one, you block that too.

Blocking sends them to Spam, it doesn't bounce or notify them, so they won't know. If you want Google to actually action the sender, hit 'Report spam' as well as blocking.

It's per-address, so a determined sender just makes a new Gmail. For those, a filter that auto-deletes emails containing certain words works better than blocking one address at a time.