This survey is a general overview of modern optical studies of the Moon and their diagnostic meaning. It includes three united parts: phase photometry, spectrophotometry, and polarimetry. The first one is devoted to the progress in the photometry of the Moon, which includes absolute albedo determination to refine the albedo scale (e.g., to connect lunar observations and the data of lunar sample measurements) and mapping the parameters of a lunar photometric function (e.g., the phase-angle ratios method) with the aim of making qualitative estimates of regolith structure variations. This part also includes observations of the lunar opposition effect as well as photogrammetry and photoclinometry techniques. In particular, available data show that because of the low albedo of the lunar surface, the coherent backscattering enhancement hardly influences the lunar opposition spike, with the exception of the brightest lunar areas measured in the NIR. The second part is devoted to chemical/mineral mapping of the Moon's surface using spectrophotometric measurements. This section also includes analyses related to the detection of water ice or hydroxyl, prognoses of maturity, and helium-3 abundance mapping. In particular, we examine the relationship between superficial OH/H2O compounds spectrally detected recently and bulk “water ice” found earlier by the Lunar Prospector GRS and LRO LEND, assuming that the compounds are delivered to cold traps (permanently shadowed regions) with electrostatically levitated dust saturated by solar wind hydrogen. Significant problems arise with the determination of TiO2 content, as the correlation between this parameter and the color ratio C(750/415nm) is very non-linear and not universal for different composition types of the lunar surface; a promising way to resolve this problem is to use color ratios in the UV spectral range. The third part is devoted to mapping of polarization parameters of the lunar surface, which enable estimates of the average size of regolith particles and their optical inhomogeneity. This includes considerations of the Umov effect and results of spectropolarimetry, negative polarization imagery, and measurements of other polarimetric parameters, including the third Stokes parameter. Although these three research divisions have not been developed equally and the numbers of proper references are very different, we try to keep a balance between them, depicting a uniform picture. It should be emphasized that many results presented in this review can be applied to other atmosphereless celestial bodies as well.