Benford's Law (BL), a notorious gem of mathematics folklore, asserts that leading digits of numerical data are usually not equidistributed, as might be expected, but rather follow one particular logarithmic distribution. Since first recorded by Newcomb, this apparently counterintuitive observation has been discussed widely under various aspects. In allusion to the splendid tradition of interplay between dynamical systems and (metric) number theory, it is natural to ask whether dynamical systems can actually generate numerical data exhibiting Benford's logarithmic distribution and whether in turn something about dynamics can be learned from BL. Both questions have attracted considerable interest recently, and both are answered in the affirmative in this talk. Our analysis proceeds via a combination of deterministic and probabilistic techniques. We explain why BL, at least in its strict form, should not be expected to hold for classical "chaotic" systems, we discuss several examples and applications which provide a clear appreciation of BL's surprising ubiquity, and we mention a few challenging open problems.