In the paper a survey of the asymptotic theory of recursive estimation of probability densities is given. Stress is laid on pointwise properties. In particular, asymptotic unbiasedness and consistency under possibly minimal assumptions and the rates of convergence of the mean square error, laws of theiterated logarithm and Berry-Esseen type theorems under suitably stronger assumptions are discussed for the estimators in question. The paper is a slightly modified version of an earlier paper of the second author (to appear in "Sequential methods in statistics", R.Zieliński fed.J, Banach Center Publications, vol. 16 , PVN - Polish Scientific Publishers)
