Not sure if this is what you were asking, but there are several configurations where there are no lifters (or at least, no push-rods) in an engine, where the valves are driven either through rocker arms or directly by the camshaft(s). Such a configuration is an OHC (overhead cam) configuration. SOHC are higher performance and lighter (and so typically have a higher rev range) than underhead cams with lifters. In SOHC (single overhead cam) setups you'll see a single camshaft driving rocker arms that actuate the valves:
Whereas in DOHC (dual overhead cam) setups you'll see two cams directly driving the valves:
DOHC valvetrains give the highest performance of conventional setups, and have the lowest inertia and so highest rev range, but they are somewhat more difficult to service due to the fact you need to keep the timing of the two camshafts in sync as well as each camshaft to the crankshaft timing. Not only that, the valve clearances on a SOHC can usually be adjusted by turning adjuster screws on the rocker arms, where on DOHC valvetrains you need to replace shims on the tappets to adjust valve clearance, which usually involves removing the camshaft(s).
Now for tappets, you'll see shim-over-bucket, shim-under-bucket, hemispherical, and desmodromic (pretty much Ducati engines only, but very cool).
Shim-over-bucket has a spacer shim on top of the tappet that is the contact piece for the camshaft or rocker arm, but this picture illustrates one of the downsides of this setup:
At high speeds in DOHC configurations, it is possible for the swiping of the cam lobe across the shim to cause it to pop out of its slot and cause damage to the valvetrain.
This problem is solved by shim-under-bucket tappets, which are similar but the shim is under the bucket (hence the name):
Also seen here:
There isn't a downside to using these as opposed to shim-over-bucket, except for the fact that shims can sometimes be removed from shim-over-bucket tappets without removing the camshaft, which makes service easier.
Now for hemispherical tappets:
The main point is to make service easier, as in these setups there's an arm that's anchored to the cylinder head that has its end between the camshaft and valve, and has a hemispherical shim that sits in a depression in the arm, like so:
The arm can be removed very quickly by removing a clip and sliding it off to the side, rather than needing to remove the camshaft, but this system still allows for a DOHC valvetrain. Notice the dual valve springs in the picture. This is to reduce the amount of time it takes for the valve to return once opened in order to reduce the possibility of valve float and therefore, again, raise the potential rev limit.
Finally, Ducati's desmodromic valves:
These are about as complicated as they look. This uses three camshafts, where the two on the ends are responsible for directly opening the valves, and the camshaft in the center is responsible for forcing the valves closed again via rocker arms. This (in theory and for the most part in practice) eliminates valve float and removes valvetrain inertia as a rev limiting factor. This means that you may see insane (20k!) redlines on engines with desmodromic valves. However, they are AWFUL to service (in my opinion), due to the number of moving parts and shims.
I hope this all helped!