Species traits and environmental conditions determine the existence and strength of trophic interactions, but how they do so is poorly understood. To enable the informed inclusion of such driving factors in dynamic trophic-interaction models, we revisit and expand the functional and numerical response functions using a modular approach which is readily integrated into existing models. We divide the trophic interaction between predator and prey into eight steps: (1) search, (2) prey detection, (3) attack decision, (4) pursuit, (5) subjugation, (6) ingestion, (7) digestion, and (8) nutrient allocation. Formulating this as a modular functional-response function, we build a general dynamical model where trophic interactions can be explicitly parameterized for multiple traits and environmental factors. We then concretize this approach by outlining how a specific community can be modeled by selecting key modules (steps) and parameterizing them for relevant factors. This we exemplify for a community of terrestrial arthropods using empirical data on body size and temperature responses. With species interactions at the core of community dynamics, our modular approach allows for quantification and comparisons of the importance of different steps, traits, and abiotic factors across ecosystems and trophic interaction types, and provides a powerful tool for trait-based prediction of food-web structure and dynamics.