  Differently from passive Brownian particles, active particles, also known as
self-propelled Brownian particles or microswimmers and nanoswimmers, are
capable of taking up energy from their environment and converting it into
directed motion. Because of this constant flow of energy, their behavior can
only be explained and understood within the framework of nonequilibrium
physics. In the biological realm, many cells perform directed motion, for
example, as a way to browse for nutrients or to avoid toxins. Inspired by these
motile microorganisms, researchers have been developing artificial particles
that feature similar swimming behaviors based on different mechanisms; these
manmade micro- and nanomachines hold a great potential as autonomous agents for
healthcare, sustainability, and security applications. With a focus on the
basic physical features of the interactions of self-propelled Brownian
particles with a crowded and complex environment, this comprehensive review
will put the reader at the very forefront of the field, providing a guided tour
through its basic principles, the development of artificial self-propelling
micro- and nanoparticles, and their application to the study of nonequilibrium
phenomena, as well as the open challenges that the field is currently facing.
