Homogeneous spaces are manifolds with many symmetries, and as
such they are a fantastic playground for mathematical models ranging from
general relativity to solid state physics. In this talk, I will give a
non-technical approach to the different types of symmetries that one likes
to consider - like reflections, special properties of geodesics,
curvature, or differential operators - with many examples and
applications. In the last part, I will present some recent classification
results on certain classes of homogeneous spaces, and why they are
interesting.

The talk is suitable as an introduction to the vast area of homogeneous
spaces for non-experts.