You can route through the night and into the next day(s) by navigating to the Driver Profile's tab, and editing the drivers whose routes will carry over into the next day.
Using military time, adjust their Availability so that their shift time continues into the following day. For example, a driver whose shift starts at 2pm, and ends the midnight after next would be represented with a shift start of 14:00 and shift end of 48:00.
In the Timeline, a +1 will appear to represent that this part of the route takes place on the next day.
The shift time can go all the way up to 99:00 if you'd like to route over multiple nights. That means there is a 99 hour limit for multi-day routes.