Billiards corresponding to planar periodic Lorentz processes are considered in the usual
(hard) sense and in the case when the hard core potential of the scatterers is replaced
by some other circularly symmetric potential. A review on certain important aspects of
the history of the subject is given and some new results on exponential decay of
correlations are formulated. Both the results from the literature and those of our
own mentioned are mathematically rigorous, nevertheless, proofs are only briefly
sketched. For further details, see the preprint [Correlation decay in certain soft
billiards, Commun. Math. Phys., in press].