When exposed to a partially wetting liquid, many natural and artificial surfaces equipped with complex topographies display a rich variety of liquid interfacial morphologies. In the present article, we focus on a few simple paradigmatic surface topographies and elaborate on the statics and dynamics of the resulting wetting morphologies. It is demonstrated that the spectrum of wetting morphologies increases with increasing complexity of the groove structure. On elastically deformable substrates, additional structures in the liquid morphologies can be observed, which are caused by deformations of the groove geometry in the presence of capillary forces. The emergence of certain liquid morphologies in grooves can be actively controlled by changes in wettability and geometry. For electrically conducting solid substrates, the apparent contact angle can be varied by electrowetting. This allows, depending on groove geometry, a reversible or irreversible transport of liquid along surface grooves. In the case of irreversible liquid transport in triangular grooves, the dynamics of the emerging instability is sensitive to the apparent hydrodynamic slip at the substrate. On elastic substrates, the geometry can be varied in a straightforward manner by stretching or relaxing the sample. The imbibition velocity in deformable grooves is significantly reduced compared to solid grooves, which is a result of the microscopic deformation of the elastic groove material close to the three phase contact line.