I know the US Air Force intends to replace its jet fighter trainers sometime soon. What will take their place and when is that supposed to happen? Can you give me any details about the program in a quick summary?
The U.S. Air Force issued a request for new supersonic jet fighter training aircraft in 2015. Several companies (and joint ventures) entered the competition. Ultimately, the Boeing-Saab team was selected as the winner in 2018. Their design, later dubbed the T-7 Red Hawk, is slated to become the newest USAF training aircraft. 

The T-7 has a relatively conventional configuration, with swept wings and two tailfins framing a single General Electric F404-GE-103 afterburning turbofan engine. Though a single engine sounds like a downgrade from the current T-38 Talon's two engines, this F404 actually produces three times as much thrust as both of the T-38's combined. The Red Hawk will carry two pilots (typically a student and an instructor). Since it’s intended to train pilots on advanced 4th- and 5th-generation fighters, it will simulate many of their systems such as radar, data links, defensive capabilities, etc., even though the T-7 doesn’t carry those systems itself. 

Originally, the new trainer was expected to enter service in the year 2020, but delays have pushed its delivery date to 2025 at the earliest. There is no estimate yet on when it will fully replace the current T-38 fleet.