Constant mean curvature surfaces and related areas of submanifold theory represent a classical field of research that uses techniques from both Differential Geometry and Geometric Analysis. The aim of this H-workshop is to gather together some distinguished geometers to discuss some cutting-edge discoveries in this field, as well as to give PhD students the opportunity to present their works. This event has been conceived as part of the project constant mean curvature surfaces in homogeneous 3-manifolds, supported by MICIN/AEI grant PID2022-142559NB-I00.