IEEE has a spot on how researchers are using jets of air to grip onto all kinds of surfaces.
There are all kinds of ways to stick to a surface, but one of the simplest is to use a gripper that operates on the Bernoulli principle. All the Bernoulli principle says is that as a liquid moves faster, its pressure decreases. For the purpose of a robotic gripper, air counts as a fluid, and if you squirt air out around the edges of a circular gripper fast enough, it’ll start to generate a vacuum force that’s strong enough to grab things without the surface of the gripper actually needing to touch them.
Check out the rest of the blog post for how this system works.