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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.
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As shown by early studies on mean-field models of the glass transition, the geometrical features of the energy landscape provide fundamental information on the dynamical transition at the Mode-Coupling temperature $T_d$. We show that active particles can serve as a useful tool for gaining insight into the topological crossover in model glass-formers. In such systems the landmark of the minima-to-saddle transition in the potential energy landscape, taking place in the proximity of $T_d$, is the critical slowing down of dynamics. Nevertheless, the critical slowing down is a bottleneck for numerical simulations and the possibility to take advantage of the new smart algorithms capable to thermalize down in the glass phase is attractive. Our proposal is to consider configurations equilibrated below the threshold and study their dynamics in the presence of a small amount of self-propulsion. As exemplified here from the study of the p-spin model, the presence of self-propulsion gives rise to critical off-equilibrium equal-time correlations at the minima-to-saddles crossover, correlations which are not hindered by the sluggish glassy dynamics.
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