In many biological applications, such as cell therapy and drug delivery, there is a need to enhance diffusion by enabling chemical transport in all three dimensions. We highlight this need by comparing diffusion in a conventional two-dimensional (2D) microwell with diffusion in a three-dimensional (3D) cubic microwell using numerical simulations. We also describe the fabrication of hollow polymeric (and biocompatible) cubic microwells and microwell arrays. We emphasize that since the assembly process is compatible with 2D lithographic patterning, porosity can be precisely patterned in all three dimensions. Hence, this platform provides considerable versatility for a variety of applications.