Current status censoring (CSC), also known as case I interval censoring, implies that the lifetime of interest is never observed. Instead it is known if the event already occurred or not at a random monitoring time. CSC is a simple sampling procedure and in many applications the only possibility to assess the lifetime of interest. For instance, serial-sacrifice carcinogenicity experiments of an occult non-lethal tumor provide an example of CSC because at the time of sacrifice the cancer may or may not be present. Further, in some applications only monitoring times for already occurred events are available, or only monitoring times for not occurred events are available. Theoretically the CSC is of a great interest because the survival function is not estimable with the parametric rate \(n^{-1}\) . Instead, it is estimated with a nonparametric rate which is slower than \(n^{-1}\) and depends on smoothness of the survival function. The CSC also slows down rate of density estimation. On the other hand, the rate for CSC regression is the same as for directly observed data. All these fascinating issues, as well as estimation of linear functionals and conditional distributions are explained and illustrated via examples.