To block all calls on an Android phone, either set notifications to None, or turn on Blocking mode in settings. The method for blocking specific numbers varies for each phone and version of Android. The easiest way to block numbers is to download an app such as Mr. Number. This free app makes it easy to block calls and texts and enables the user to report spam calls and texts to other users.
On certain versions of Android, it's possible to select the number you want to block from the call log, hit the three-dot menu icon and click Add to Reject List. This feature disables incoming calls from specific numbers but is unavailable on certain phones.
Alternate options for call- and text-blocking apps are Call Control and Extreme Call Blocker. Call Control has a large list of user-submitted spam numbers that can automatically be blocked, and it also ties in with the FCC Do Not Call registry. This app gives a free 14-day trial and then charges $8.
Another popular call-blocking app is Extreme Call Blocker. Although it's not free, its comprehensive call- and text-blocking services are among the best available. Calls can be sent directly to voicemail, picked up or hung up automatically. This app can also be used to block outgoing calls, and it features stealth and password modes to keep phone contents hidden.