In this chapter, we will compute the moments of the volumes of random beta-type simplices. For concreteness, consider a beta simplex \(\displaystyle [X_1,\dots ,X_k] \sim \operatorname {BetaSimp}(\mathbb {R}^d;\beta _1,\dots ,\beta _{k};\varDelta ^\rho ). \) In Sect. 6.1, we start with the basic case of full-dimensional simplices with independent vertices, that is \(k= d+1\) and \(\rho =0\) . In Sect. 6.2, we generalize this to full-dimensional weighted simplices with general weight exponents \(\rho \) . In Sect. 6.3, we prove the most general result by removing the requirement of full-dimensionality, i.e. we allow for arbitrary \(k\in \{2,\ldots , d+1\}\) . In Sects. 6.4 and 6.5, we represent the volume of \([X_1,\dots , X_k]\) as a product of independent univariate beta variables with appropriate parameters and show that its density can be expressed through a Meijer G-function. In Sect. 6.6, we collect various results on volumes of random simplices including condensed formulas for the expectation and the second moment of the volume, a proof of the monotonicity of the expected volume in \(\beta \) , and a comparison of various beta simplices to the regular simplex in the high-dimensional limit. We conclude Sect. 6.6 by deriving an asymptotic formula for the right tail of the beta-simplex volume.