Following Jacques Tits' geometric interpretation of the exceptional
complex Lie groups, Francis Buekenhout generalized in the late
seventies certain aspects of this theory in order to achieve a
combinatorial understanding of all finite simple groups.
Since then, two main traces have been developed in diagram geometry.
One is to classify geometries over a given diagram, mainly over
geometries extending buildings.
Another trace is to classify coset geometries for a given group
under certain conditions.

We will start the talk by explaining what an incidence geometry is.
Then we will give some examples of results obtained in the first
and the second approach. We will explain the connection between
incidence geometries and finite groups which essentially arise
as automorphism groups. We will also show how computational
algebra softwares like {\sc Magma} may be used to explore
incidence geometries and insist on the fact that experimental
work in this field has already been very fruitful and has led
to several theoretical results.