In this thesis we study examples of triple spaces, both their structure theory, their invariant differential operators as well as analysis on them. The first major results provide us with some examples of triple spaces which are strongly spherical, i.e. satisfy some conditions reminiscent of properties of symmetric spaces. The algebras of invariant differential operators for these spaces are studied and the conclusion is that most of them are non-commutative. Finally, we restrict our attention to a single triple space, giving a specific polar decomposition and corresponding integration formula, and studying the relations between open orbits of parabolic subgroups, multiplicities and distribution vectors.