Drops of twist-bend nematic liquid crystals Epifanio Virga Università di Pavia The newly discovered twist-bend nematic phase, which in certain materials condenses from the ordinary nematic upon cooling, is characterized by a peculiar ground state in which molecules precede around an axis, often called the twist axis, making a fixed angle with it (typically around 20 deg in amplitude) while remaining uniform (but with different orientations) on each plane orthogonal to the twist axis. The integral lines of the molecular director field in the ground state are helices with a nanoscopic pitch (typically around 10 nm in length). Despite their resemblance to chiral smectics, by which twist-bend nematics were at first mistaken, their mass density is uniformly distributed in space and the planes with uniform molecular alignment are by no means material layers; to mark the distinction, it has been proposed to call the latter pseudo-layers. Molecules move freely from one pseudo-layer to the next: they constitute a truly three-dimensional, anisotropic liquid. Drops of ordinary nematics surrounded by isotropic fluids have long been observed experimentally and described theoretically: they often appear in a tactoidal shape, where the surface normal exhibits two symmetric points of discontinuity. We shall see that tactoids as well as shapes with more than two points of discontinuity for the surface normal are exhibited by drops of a twist-bend nematic in contact with its nematic companion phase.