  Several techniques of generating random quantum channels, which act on the
set of $d$-dimensional quantum states, are investigated. We present three
approaches to the problem of sampling of quantum channels and show under which
conditions they become mathematically equivalent, and lead to the uniform,
Lebesgue measure on the convex set of quantum operations. We compare their
advantages and computational complexity and demonstrate which of them is
particularly suitable for numerical investigations. Additional results focus on
the spectral gap and other spectral properties of random quantum channels and
their invariant states. We compute mean values of several quantities
characterizing a given quantum channel, including its unitarity, the average
output purity and the $2$-norm coherence of a channel, averaged over the entire
set of the quantum channels with respect to the uniform measure. An ensemble of
classical stochastic matrices obtained due to super-decoherence of random
quantum stochastic maps is analyzed and their spectral properties are studied
using the Bloch representation of a classical probability vector.
