This comprehensive review focuses on the fundamental physical features of self-propelled Brownian particles in complex and crowded environments. It begins by introducing the concept of active matter, which can convert energy from its environment into directed motion, leading to novel behaviors not observed in thermally equilibrium systems. The review then delves into the behavior of non-interacting active particles in homogeneous environments, discussing models of active Brownian motion, effective diffusion coefficients, and temperature, as well as the dynamics of biological and artificial microswimmers. The section on hydrodynamics explores microhydrodynamics, particle-particle interactions, and hydrodynamic coupling to walls. The review also examines the collective behaviors of interacting particles, including clustering, self-jamming, and active turbulence. It further investigates the effects of complex environments, such as interactions with walls and obstacles, and the sorting of microswimmers. Finally, the review highlights the challenges and future directions in the field, emphasizing the need to understand collective behaviors, dynamics in real-life environments, and the scaling down to the nanoscale.This comprehensive review focuses on the fundamental physical features of self-propelled Brownian particles in complex and crowded environments. It begins by introducing the concept of active matter, which can convert energy from its environment into directed motion, leading to novel behaviors not observed in thermally equilibrium systems. The review then delves into the behavior of non-interacting active particles in homogeneous environments, discussing models of active Brownian motion, effective diffusion coefficients, and temperature, as well as the dynamics of biological and artificial microswimmers. The section on hydrodynamics explores microhydrodynamics, particle-particle interactions, and hydrodynamic coupling to walls. The review also examines the collective behaviors of interacting particles, including clustering, self-jamming, and active turbulence. It further investigates the effects of complex environments, such as interactions with walls and obstacles, and the sorting of microswimmers. Finally, the review highlights the challenges and future directions in the field, emphasizing the need to understand collective behaviors, dynamics in real-life environments, and the scaling down to the nanoscale.