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. I've had Delta wait for me after inbound connection delays on several occasions.

Generally, an airline will not delay a connecting flight for a single late passenger or even a small group, as doing so creates a "cascading" effect of delays for hundreds of other travelers and flight crews later in the day. Airlines prioritize "on-time performance" and the integrity of their network. However, there are rare exceptions in 2026: if a large number of passengers (e.g., 20+ people) are on the same delayed inbound flight, or if the connecting flight is the last departure of the night, the airline's operations center may authorize a short hold of 10–15 minutes. This decision is based on complex algorithms that calculate the cost of rebooking passengers versus the cost of a late departure. If you are running late, your best bet is to check the airline's app; if you miss the connection, most major carriers in 2026 will automatically rebook you on the next available flight and send the new boarding pass to your phone. If the delay was the airline's fault and involves an overnight stay, they are generally required to provide hotel and meal vouchers.