In this talk we will consider the real structures of certain complex algebraic varieties equipped with a reductive algebraic group action :
the horospherical varieties. We will see how to determine when such structures exist and, if so, how to describe them.
In particular, we will try to illustrate our approach on two classical families of horospherical varieties : the flag varieties and the toric varieties.
This is a joint work with Lucy Moser-Jauslin (IMB, Dijon).