We introduce the framework to determine the shape of capillary droplets and small crystals. We show how bubbles appear naturally as critical points of the capillarity energy. This result points to a possible non-smooth extension of the classical Aleksandrov Theorem to account for bubbling. Finally, we discuss recent developments on this direction using the Heintze-Karcher inequality. This is joint work with F. MAGGI, C. MIHAILA, and R. NEUMAYER.