2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/169591We review recent developments in the arithmetic of K3 surfaces. Our focus lies on aspects of modularity, Picard number and rational points. Throughout we emphasise connections to geometry.19 pages; v3: reference [5] added in section 13Algebraic GeometryNumber Theory14J28; 11F11, 11G15, 11G25, 14G05, 14G10text