One of the most common approaches for control of skin pigmentation involves the inhibition of tyrosinase, a copper-containing enzyme which catalyzes the key steps of melanogenesis. This review focuses on the tyrosinase inhibition properties of a series of natural and synthetic, bioinspired phenolic compounds that have appeared in the literature in the last five years. Both mushroom and human tyrosinase inhibitors have been considered. Among the first class, flavonoids, in particular chalcones, occupy a prominent role as natural inhibitors, followed by hydroxystilbenes (mainly resveratrol derivatives). A series of more complex phenolic compounds from a variety of sources, first of all belonging to the Moraceae family, have also been described as potent tyrosinase inhibitors. As to the synthetic compounds, hydroxycinnamic acids and chalcones again appear as the most exploited scaffolds. Several inhibition mechanisms have been reported for the described inhibitors, pointing to copper chelating and/or hydrophobic moieties as key structural requirements to achieve good inhibition properties. Emerging trends in the search for novel skin depigmenting agents, including the development of assays that could distinguish between inhibitors and potentially toxic substrates of the enzyme as well as of formulations aimed at improving the bioavailability and hence the effectiveness of well-known inhibitors, have also been addressed.