A random beta polytope is defined as a convex hull of n independent, beta-distributed points \(X_1,\ldots , X_n\) in \(\mathbb {R}^d\) . Each \(X_i\) follows a beta distribution \(f_{d,\beta _i}\) on \(\mathbb {B}^d\) with its individual parameter \(\beta _i \geq -1\) . Similarly, beta prime and Gaussian polytopes are defined as convex hulls of independent points following beta prime or Gaussian distributions on \(\mathbb {R}^d\) , with possibly different parameters. In this chapter, we will prove a version of the canonical decomposition for these random beta-type polytopes. As an application, we compute expected values of several functionals of beta-type polytopes, including the expected number of facets, the expected volume, expected surface area and, more generally, all expected intrinsic volumes. Many of these functionals are special cases of the so-called T-functional whose expectation we also determine. In addition, we discuss applications of beta-type random polytopes to spherical convex hulls and cells of random hyperplane and Voronoi tessellations.