Kurzbeschreibung: Hitting time statistics has long been a popular theme in the study of statistical limit theorems in dynamics. In hitting time statistics one fixes a shrinking sequence of targets and asks about the limiting distribution of the first hitting time function to the targets. We introduce a related question which we refer to as visiting time statistics. Here we fix the orbit and ask about the limiting distribution of target families that are "visited" by the orbit. For certain well-behaved dynamical systems we can prove that the two types of statistics behave identically. We also obtain Poisson statistics for these systems and obtain a new method of proof for hitting time statistics. In the process we make a few interesting observations about Kac' Lemma.