I will describe first basic facts on p-adic symmetric spaces, in
particular results of A.Helminck with S.P. Wang and G. Helminck.
I will describe the Cartan decomposition for p-adic symmetric spaces
(Benoist-Oh, Delorme-Sécherre).
I will describe results of Lagier, Kato-Takano and I on $H$-fixed
linear forms on smooth-modules and Jacquet modules. This leads to the
definition of the constant term of smooth functions on a p-adic
symmetric space and of cuspidal functions. Actually all of this works
also for mixed models, which include Whittaker models and reductive
symmetric spaces. Finiteness theorems will be described.
The rational continuation of Eisenstein integrals will be described
(Blanc-Delorme).