The first unambiguous detection of meteoroids impacting the night side of the Moon was obtained during the 1999 Leonid storm. Up to eight optical flashes were recorded with CCD video cameras attached to small telescopes on November 18, 1999. Six impacts were videotaped by at least two independent observers at the same times and lunar locations, which is perhaps the strongest evidence for their collisional nature. The flashes were clearly above the noise and lasted for less than 0.02 s. Although previous observational efforts did not succeed in detecting impact flashes, additional candidates have been reported in the literature. The evidence accumulated so far implies that small telescopes equipped with high speed cameras can be used as a new tool for studying meteoroid streams, sporadic meteoroids, and hypervelocity collisions. In this review we discuss the various intervening parameters for detectability of flashes on the night side of the Moon (geometrical effects, contamination by scattered light from the day side, and properties of the meteoroids such as speed and flux of particles). Particular emphasis is placed on the analysis of the observations in order to derive relevant physical parameters such as luminous efficiencies, impactor masses, and crater sizes. Some of these parameters are of interest for constraining theoretical impact models. From a simple analysis, it is possible to derive the mass distribution of the impactors in the kg range. A more elaborate analysis of the data permits an estimate of the fraction of kinetic energy converted to radiation (luminous efficiency) if the meteoroid flux on the Moon is known. Applied to the 1999 lunar Leonids, these methods yield a mass index of 1.6 +/- 0.1 and luminous efficiencies of 2 × 10^-3 with an uncertainty of about one order of magnitude. Predictions of visibility of the major annual meteor showers are given for the next few years. These include the forthcoming 2001 Leonid return, for which we estimate detection rates in the visible.