Many molecules in living cells are present in such low numbers that individual probabilistic chemical events can have a great randomizing effect on the whole system. I will describe how this radically changes the dynamics of several core cellular processes, from cell fate decisions to the oscillators and DNA repair. The presentation will convey some analytical results for classes of stochatic processes, with an emphasis on unsolved problems, but also experimental results, aimed at a board audience, to illustrate what is known about these processes.