  We derive a mode-coupling theory for the slow dynamics of fluids confined in
disordered porous media represented by spherical particles randomly placed in
space. Its equations display the usual nonlinear structure met in this
theoretical framework, except for a linear contribution to the memory kernel
which adds to the usual quadratic term. The coupling coefficients involve
structural quantities which are specific of fluids evolving in random
environments and have expressions which are consistent with those found in
related problems. Numerical solutions for two simple models with pure hard core
interactions lead to the prediction of a variety of glass transition scenarios,
which are either continuous or discontinuous and include the possibility of
higher-order singularities and glass-glass transitions. The main features of
the dynamics in the two most generic cases are reviewed and illustrated with
detailed computations. Moreover, a reentry phenomenon is predicted in the low
fluid-high matrix density regime and is interpreted as the signature of a
decorrelation mechanism by fluid-fluid collisions competing with the
localization effect of the solid matrix.
