From a geometrical perspective, a chiral object does not have mirror planes or inversion symmetry. It exhibits the same physical properties as its mirror image (enantiomer), except for the chiroptical activity, which is often the opposite. Recent advancements have identified particularly interesting implications of chirality on the optical properties of metal nanoparticles, which are intimately related to localized surface plasmon resonance phenomena. Although such resonances are usually independent of the circular polarization of light, specific strategies have been applied to induce chirality, both in assemblies and at the single-particle level. In this tutorial review, we discuss the origin of plasmonic chirality, as well as theoretical models that have been proposed to explain it. We then summarise recent developments in the synthesis of discrete nanoparticles with plasmonic chirality by means of wet-chemistry methods. We conclude with a discussion of promising applications for discrete chiral nanoparticles. We expect this tutorial review to be of interest to researchers from a wide variety of disciplines where chiral plasmonics can be exploited at the nanoparticle level, such as chemical sensing, photocatalysis, photodynamic or photothermal therapies, etc.