  We study the spectral properties of the Dirichlet-to-Neumann operator and the
related Steklov problem in spheroidal domains ranging from a needle to a disk.
An explicit matrix representation of this operator for both interior and
exterior problems is derived. We show how the anisotropy of spheroids affects
the eigenvalues and eigenfunctions of the operator. As examples of physical
applications, we discuss diffusion-controlled reactions on spheroidal partially
reactive targets and the statistics of encounters between the diffusing
particle and the spheroidal boundary.
