Turbulence may enhance contact rates between planktonic predators and their prey. We formulate simple and general models of prey encounter rates, taking into account the behaviours and motility patterns of both prey and predator as well as turbulent fluid motion. Using these models we determine the levels of turbulence (as dissipation rate) at which ambient fluid motion is important in enhancing prey encounter rates for various types of predators (e.g, ambush and cruise predators, suspension feeders). Generally, turbulence has the largest effect on prey encounters for predators with low motility and long reaction distances. Also, turbulence is most important for meso-sized (mm to cm) predators and insignificant for smaller and larger predators. The effect of turbulence on copepods is specifically examined. For copepods that establish feeding currents, turbulence is of minor importance; for ambush feeding copepods, such as Acartidae and many cyclopoids, turbulence has a dominant influence on prey encounter rates. The effect on cruising predators is intermediate. Application of the models to situations examined experimentally demonstrates a high predictive performance. Finally we explore and model the potentially negative effects of turbulence on copepod feeding currents, prey perception and capture success. At typical and even high turbulent intensities, none of these is significantly affected.