  In this work we systematically investigate the condensate properties,
superfluid properties and quantum phase transitions in interacting Bose gases
trapped in disordered optical potentials. We numerically solve the Bose-Hubbard
Hamiltonian exactly for different: (a) types of disorder, (b) disorder
strengths, and (c) interatomic interactions. The three types of disorder
studied are: quasiperiodic disorder, uniform random disorder and random
speckle-type disorder. We find that the Bose glass, as identified by Fisher et
al [Phys. Rev. B {\bf 40}, 546 (1989)], contains a normal condensate component
and we show how the three different factors listed above affect it.
