Swimming in Complex Fluids

We review the literature on swimming in complex fluids. A classification is proposed by comparing the length and timescales of a swimmer with those of nearby obstacles, interpreted broadly, extending from rigid or soft confining boundaries to molecules that confer the bulk fluid with complex stresses. A third dimension in the classification is the concentration of swimmers, which incorporates fluids whose complexity arises purely by the collective motion of swimming organisms. For each of the eight system classes that we identify, we provide a background and describe modern research findings. Although some classes have seen a great deal of attention for decades, others remain uncharted waters still open and awaiting exploration. Expected final online publication date for the Annual Review of Condensed Matter Physics, Volume 14 is March 2023. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.