A large number of suspension-feeding aquatic animals (e.g. bivalves, polychaetes, ascidians, bryozoans, crustaceans, sponges, echinoderms, cnidarians) have specialized in grazing on not only the 2 to 200 μm phytoplankton but frequently also the 0.5 to 2 μm free-living bacteria, or they have specialized in capturing larger prey, e.g. zooplankton organisms. We review the different particle capture mechanisms in order to illustrate the many solutions to the common problem of obtaining nourishment from a dilute suspension of microscopic food particles. Despite the many differences in morphology and living conditions, particle capture mechanisms may be divided into 2 main types. (1) Filtering or sieving (e.g. through mucus nets, stiff cilia, filter setae), which is found in passive suspension feeders that rely on external currents to bring suspended particles to the filter, and in active suspension feeders that themselves produce a feeding flow by a variety of pump systems. Here the inventiveness of nature does not lie in the capture mechanism but in the type of pump system and filter pore-size. (2) A paddle-like flow manipulating system (e.g. cilia, cirri, tentacles, hair-bearing appendages) that acts to redirect an approaching suspended particle, often along with a surrounding ‘fluid parcel’, to a strategic location for arrest or further transport. Examples include (1) sieving (e.g. by microvilli in sponge choanocytes, mucus nets in polychaetes, acidians, and salps among others), filter setae in crustaceans, ‘ciliary sieving’ by stiff laterofrontal cilia in bryozoans and phoronids; and (2) ‘cirri trapping’ in mussels and other bivalves with eu-laterofrontal cirri, ciliary ‘catch-up’ in bivalve and gastropod veliger larvae, some polychaetes, entroprocts, and cycliophores. These capture mechanisms may involve contact with a particle, and possibly mechanoreception or chemoreception, or may include redirection of particles by the interaction of multiple currents (e.g. in scallops and other bivalves without eu-laterofrontal cirri). Based on the review, we discuss the current physical and biological understanding of the capture process and suggest a number of specific problems related to particle capture, which may be solved in the future using advanced theoretical, computational and experimental techniques.