The survival of many microorganisms depends on their ability to navigate through complex biological environments. Complex fluid phenomena like viscoelasticity and anisotropy can have unexpected and important consequences for motility. We will discuss analytical and numerical insights into swimming through model viscoelastic and anisotropic fluids, with a special focus on the outsized roles played by the presence of nearby boundaries. And we will propose a classification which seeks to place a multitude of systems based on the relative size and timescale of active bodies and surrounding obstacles, broadly interpreted.