The airline may choose to accommodate you by booking you on another flight, but that's their discretion, and you may be on the hook for change fees or even fare differences. If you miss a connection because your first flight was delayed, you're entitled to compensation depending on what caused the delay.
Do airlines hold flights for delayed passengers?
It varies. They will often wait a little while, especially if it's the last flight of the day and even moreso if there are multiple passengers making the same connection.