I will describe a series of results obtained in the last years in collaboration with Artur Avila on statistical properties of unimodal maps: for most parameters in typical analytic families of unimodal maps the corresponding map is either regular or Collet-Eckmann with slow recurrence of the critical orbit. In both cases there is a unique SRB measure for this map. We show that typically the critical orbit belongs to the basin of this measure. Moreover we prove a combinatorial formula for the eigenvalues of periodic orbits of typical nonregular analytic unimodal map. We also estimate fractal dimensions of some exceptional sets of parameters associated to such families. Co-author: Artur Avila.