We report in this review the experimental observations that led us to claim the occurrence of Bose-Einstein condensation for polaritons in microcavities. First, we will recall the properties of microcavity polaritons that are of interest for Bose condensation. Then, we will list the observed properties in the highest quality sample that we have been able to study a CdTe monolithic microcavity. In this sample, that shows a very large Rabi splitting of 26 meV, we first observe a thermalized distribution of polaritons below threshold. At threshold, observed to occur for ground-state occupation factors of the order of 1, we observe a strong increase of the ground-state emission. At the same density, a strong reduction of the linewidth and a build-up of the first-order coherence are observed. Also, the distribution of the polaritons appears to change from Boltzmann-like to a Bose-like distribution. Polarization of the emission is observed that is not due to spontaneous symmetry breaking but to a slight birefringence of the material. Second-order coherence shows that the polariton condensate still contains a significant excitonic fraction. The main observation in favor of BEC is the clear evidence for long-range spatial coherence of the whole polariton gas. This measurement is obtained through the use of a specially designed Michelson interferometer. Importantly enough, we discuss the possible similarities and differences between a polariton condensate and a Vertical Cavity Surface Emitting Laser (VCSEL). Although many of the properties that we have observed might show similar behavior for a VCSEL-like laser, some of the differences clearly allow to differentiate a polariton condensate from a standard laser. According to the accepted terminology, as we are observing a thermalized distribution below threshold, what we observe is not a polariton laser but a Bose-Einstein condensate indeed. Eventually, we study some of the consequences of the inherent disorder in semiconductor microstructures. This brings along some important observations. The first one is mode synchronization that allows the condensate to overcome residual disorder. The second one is the observation of pinned vortices, an indication of possible superfluid-like effects in the presence of disorder.