  A review of the principles of observational testing of cosmological theories
is given with a special emphasis on the distinction between observational facts
and theoretical hypotheses. A classification of modern cosmological theories
and possible observational tests for these theories is presented. The main
rival cosmological models are analyzed from the point of view of observational
testing of their initial hypothesis. A comparison of modern observational data
with theoretical predictions is presented. In particular we discuss in detail
the validity of the two basic assumptions of modern cosmology that are the
Cosmological Principle and the Expanding Space Paradigm. It is found that
classical paradigms need to be reanalyzed and that it is necessary to develop
crucial cosmological tests to discriminate alternative theories.
