We present results of our search for free floating brown dwarfs in the Pleiades star cluster showing that the process of star formation does not stop at the substellar limit. A number of objects with masses below 70 Jupiter masses have been discovered by our group (Rebolo et al. 1995 Nature 377, 129; 1996, ApJ, 469, L53). The new extension of the deep CCD survey has covered an area of 1 square degree in the cluster. Our infrared photometry and spectroscopic follow-up has shown that the newly discovered objects are indeed very cool dwarfs that at the age of the cluster must be brown dwarfs. We discuss direct evidence for the absence of hydrogen burning in the interiors of these fully convective objects based on the detection of lithium in their atmospheres. Brown dwarfs appear to be rather numerous in the cluster. We combine the results of our search with those of other surveys in order to derive the mass function beyond the substellar limit. The impact on the dark matter problem will be discussed.