Our Moon is drifting away from the Earth at approximately 3.8cm per year. Scientists know exactly how fast because of the Lunar Laser Ranging Experiment. This effect is due to tidal interactions between the Earth and the Moon. The ocean closer to the Moon actually bulges toward it. Because of the planetary rotation of the Earth and the gravitational interplay between the Earth and the Moon, the Moon is pulled faster along its orbital path. This boost in speed slowly pushes the Moon into a larger orbit. It also means that the Earth’s rotation is ever so slightly slowing down.
If you’re wondering if the moon will eventually escape Earth orbit and go spiraling away, it won’t. One reasson is that it won’t have time, because the sun will go nova and destroy the solar system in about 5 billion years. But if that didn’t happen, the moon would keep moving away for about 50 billion years, when it would stabilize and the moon and Earth would tecome tidally locked - meaning one side of the Earth would always face the moon. At that point the moon would slowly begin moving back toward Earth. Then somehow it would eventually get torn apart by gravitational effects - I don’t understand that part, it’s just what I’ve read.