In a recent preprint, Sakellaridis and Venkatesh considered the spectral decomposition of the space $L^2(X)$, where $X = H\backslash G$ is a spherical variety, $G$ is a real or $p$-adic group, and stated a conjecture describing this decomposition in terms of a dual group $\check{G}_X$ associated to $X$. In this talk we describe a way of verifying the above conjecture in many cases when $X$ has low rank, using the theory of dual pairs. We will also describe some examples that go beyond the scope of this theory. This is joint work with Wee Teck Gan.