In this chapter, we study phenomena associated with capillary forces interacting with a soft, deformable body. This interplay of surface tension and elasticity occurs in a wide variety of situations, including ones that involve the deformation of sheets and fibers. We introduce the concept of surface tension and discuss typical phenomena, such as the wetting of soft substrates; capillary adhesion; surface-tension-induced bending, buckling or wrinkling of structures; and a prototype of capillary flow, namely imbibition. We provide quantitative models to explain the observations, including using dimensional analysis and order-of-magnitude estimates, and present many cases where the predictions of the models are compared with experimental results. These ideas permeate many fields, and we have tried to capture the spirit and beauty of the subject.