  In recent years various results about locally symmetric manifolds were proven
using probabilistic approaches. One of the approaches is to consider random
manifolds by associating a probability measure to the space of discrete
subgroups of the isometry Lie group. The main goals are to prove results about
deterministic groups and manifolds by considering appropriate measures. In this
overview paper we describe several such results, observing the evolution
process of the measures involved. Starting with a result whose proof considered
finitely supported measures (more precisely, measures supported on finitely
many conjugacy classes) and proceeding with results which were outcome of the
successful and popular theory of IRS (invariant random subgroups). In the last
couple of years the theory has expanded to SRS (stationary random subgroups)
allowing to deal with a lot more problems and establish stronger results. In
the last section we shall review a very recent (yet unpublished) result whose
proof make use of random subgroups which are not even stationary.
