There are currently five major varieties of engines in use and their heads vary quite markedly.

Two-stroke engines are the simplest. They have no valves in the head or cylinder, as the gases are controlled by the piston covering and uncovering ports on the sides of the barrel. The head is usually just a flat piece of metal with a hole in it for a spark plug.

Sidevalve engines were most popular in the 1930s, and under the guise of flathead designs, survived into the 1970s especially in large-capacity American designs. They don't have valves in the head, they have them in the inlet and exhaust tracts. This means that the head is easy to machine, but limits the compression ratio that can be achieved, and thus limits the efficiency. They're called flathead engines because the head is flat.

Overhead valve engines are the next most complex; they use an arrangement of tappets and pushrods to allow the crankshaft to more-or-less directly operate the valves in the head of the engine. They are capable of much higher compression than sidevalve engines but the manufacture of the head is much more involved. You can't actually see the head on an overhead valve engine because it's obscured by the rocker cover, which is where all the gubbins for adjusting the valves and their pushrods lives.

Overhead cam engines put a camshaft or pair of camshafts (in dual overhead cam engines) above the head. This greatly reduces moving part count and removes a lot of need for adjustment. The camshafts live underneath the cover on top of the head. Because the valves are operated directly from the cams, there's a lot more room for more valves, bigger valves, and more variation in timing is possible.

Hydraulic valvegear is the Next Big Thing. It promises to bring head complexity back to sidevalve levels while giving all the benefits of overhead cams. We'll see, if and when they actually get it working...