Different applications are usually characterized by different observation distributions. There are many observation distributions defined for HSMMs in the literature. A mixture of distributions is often used to describe complexly distributed observations or a compounded observation distribution. A multispace probability distribution is applied to express a composition of different dimensional observation spaces, or a mixture of continuous and discrete ones. A segmental model is used to describe parametric trajectories that change over time. An event sequence model is used to model and analyze event-based random processes. This chapter presents all these typical observation distributions.