They are on a six-month mission, and despite the conflict in Ukraine, space remains one of the few areas of tight cooperation between the US and Russia.
The three men and one women are aboard a capsule that Elon Musk’s SpaceX company has already used four times in space.
They have a number of experiments planned.
As it is not feasible to produce artificial human organ replicas on Earth, their research will involve doing so in order to study degenerative illnesses in a low-gravity environment.
On Monday at 03:53 GMT, the crew launched from the Kennedy Space Center in Florida at 22:53 local time.