Many animals are predator and prey at the same time. This dual position represents a fundamental dilemma because gathering food often leads to increased exposure to predators. The optimization of the tradeoff between eating and not being eaten depends strongly on the sensing, feeding, and mechanisms for mobility of the parties involved. Here, I describe the mechanisms of sensing, escaping predators, and capturing prey in marine pelagic copepods. I demonstrate that feeding tradeoffs vary with feeding mode, and I describe simple fluid mechanical models that are used to quantify these tradeoffs and review observations and experiments that support the assumptions and test the predictions. I conclude by presenting a mechanistically underpinned model that predicts optimal foraging behaviors and the resulting size-scaling and magnitude of copepods' clearance rates.