Let $G$ be a reductive group. A homogeneous$G$-variety $X=G/H$ is said to be spherical if a Borel subgroup of $G$ acts with an open orbit on $X$. I'll discuss harmonic analysis on spherical varieties over $p$-adicfields (joint work with Yiannis Sakellaridis, althoughI will also review results that are solely due to Sakellaridis). Forexample
