Almost all cosmologists accept nowadays that the redshift of the galaxies is due to the expansion of the Universe (cosmological redshift), plus some Doppler effect of peculiar motions, but can we be sure of this fact by means of some other independent cosmological test? Here I will review some recent tests: CMBR temperature versus redshift, time dilation, the Hubble diagram, the Tolman or surface brightness test, the angular size test, the UV surface brightness limit and the Alcock-Paczynski test. Some tests favour expansion and others favour a static Universe. Almost all the cosmological tests are susceptible to the evolution of galaxies and/or other effects. Tolman or angular size tests need to assume very strong evolution of galaxy sizes to fit the data with the standard cosmology, whereas the Alcock-Paczynski test, an evaluation of the ratio of observed angular size to radial/redshift size, is independent of it.