  The ability of many living systems to actively self-propel underlies critical
biomedical, environmental, and industrial processes. While such active
transport is well-studied in uniform settings, environmental complexities such
as geometric constraints, mechanical cues, and external stimuli such as
chemical gradients and fluid flow can strongly influence transport. In this
chapter, we describe recent progress in the study of active transport in such
complex environments, focusing on two prominent biological systems -- bacteria
and eukaryotic cells -- as archetypes of active matter. We review research
findings highlighting how environmental factors can fundamentally alter
cellular motility, hindering or promoting active transport in unexpected ways,
and giving rise to fascinating behaviors such as directed migration and
large-scale clustering. In parallel, we describe specific open questions and
promising avenues for future research. Furthermore, given the diverse forms of
active matter -- ranging from enzymes and driven biopolymer assemblies, to
microorganisms and synthetic microswimmers, to larger animals and even robots
-- we also describe connections to other active systems as well as more general
theoretical/computational models of transport processes in complex
environments.
