They have a main structural advantage:
Mid mounted wings have the advantage of being structurally efficient when aerospace engineers desire to incorporate a swept or tapered wing design on the aircraft. This increase in structural integrity is essential for aircraft that perform extreme maneuvers or aerobatics
Source: Student Pilot News
They also leave the aircraft free of spars on the belly and room for cargo. And they reduce the induced drag
The main disadvantage is the speed. The fastest planes use low-wings. Also many of this aircraft use spars in the middle of the fuselage, so you have to have a bigger fuselage and thus more weight.
It is aerodynamically the cleanest and most balanced, but the carry-through spar can reduce the useful fuselage volume near its centre of gravity, where space is often in most demand. It is common on high-performance types such as sailplanes.
A low wing allows the pilot to have a good visibility and a lighter structure because as it is below fuselage, it doesn't have to carry more weight. But there's also a main disadvantage which occurs when landing; it produces a strong ground effect compared to the high and mid-wing. In case of an emergency you can step out and can be used as overwing exits. And finally, they have better flexibility.
A high wing provides also good visibility and lateral stability. Also increases ground clearance for the engines and cargo.
More info can be found here and here.