For every action there is an equal and opposite reaction.
The ground which pushes back on the abutments creates a resistance which is passed from stone to stone, until it is eventually pushing on the key stone which is supporting the load.

Arch types are few -- after all, an arch is an arch is an arch.
The only real subcategories come in the form of cosmetic design.
There are, for example, Roman, Baroque and Renaissance arches, all of which are architecturally different but structurally the same.

Arches are fascinating in that they are a truly natural form of bridge.
It is the shape of the structure that gives it its strength.
An arch bridge doesn't need additional supports or cables.
In fact, an arch made of stone doesn't even need mortar.
Ancient Romans built arch bridges (and aqueducts) that are still standing, and structurally sound, today.
These bridges and aqueducts are real testaments to the natural effectiveness of an arch as a bridge structure.

Arch bridges

Arch bridges are one of the oldest types of bridges and have been around for thousands of years. Arch bridges have great natural strength.

They were originally built of stone or brick but these days are built of reinforced concrete or steel. The introduction of these new materials allow arch bridges to be longer with lower spans.

Instead of pushing straight down, the load of an arch bridge is carried outward along the curve of the arch to the supports at each end. The weight is transferred to the supports at either end.

These supports, called abutments, carry the load and keep the ends of the bridge from spreading out.

The load at the top of the key stone makes each stone on the arch of the bridge press on the one next to it.
This happens until the push is applied to the end supports or abutments, which are enbedded in the ground.
The design of the arch, the semicircle, naturally diverts the weight from the bridge deck to the abutments.

The ground around the abutments is squeezed and pushes back on the abutments.

Compression
Arch bridges are always under compression. The force of compression is pushed outward along the curve of the arch toward the abutments.

Tension
The tension in an arch is negligible. The natural curve of the arch and its ability to dissipate the force outward greatly reduces the effects of tension on the underside of the arch. The greater the degree of curvature (the larger the semicircle of the arch), however, the greater the effects of tension on the underside.

Dissipation
As we just mentioned, the shape of the arch itself is all that is needed to effectively dissipate the weight from the center of the deck to the abutments. As with the beam bridge, the limits of size will eventually overtake the natural strength of the arch.