<p>Conducting polymers and other organic conductors enable emerging applications in bioelectronics, neuromorphic computing, energy storage and thermoelectric devices. When used in organic electrochemical transistors or other devices, these materials are typically doped in their bulk to very high carrier densities of the order of 10²⁰–10²¹ cm⁻³. In this regime, they show fascinating nonlinear, many-body and non-equilibrium transport phenomena that are being exploited in these applications, but whose fundamental origins remain poorly understood. In this Review, we focus on the underlying charge transport physics, examining how complex microstructure, electron–electron interactions and electron–dopant counterion interactions govern transport behaviour, including the evolution of the density of states with carrier density. We also discuss reliable experimental methods for determining carrier concentrations and measuring transport coefficients. An in-depth understanding of the charge transport physics in this high-carrier-density regime is a prerequisite for harnessing these transport phenomena in device applications.</p>