The conventional way of describing grazing in plankton models is based on a zooplankton functional response framework, according to which the consumption rate is computed as the product of a certain function of food (the functional response) and the density/biomass of herbivorous zooplankton. A large amount of literature on experimental feeding reports the existence of a zooplankton functional response in microcosms and small mesocosms, which goes a long way towards explaining the popularity of this framework both in mean-field (e.g. NPZD models) and spatially resolved models. On the other hand, the complex foraging behaviour of zooplankton (feeding cycles) as well as spatial heterogeneity of food and grazer distributions (plankton patchiness) across time and space scales raise questions as to the existence of a functional response of herbivores in vivo. In the current review, we discuss limitations of the 'classical' zooplankton functional response and consider possible ways to amend this framework to cope with the complexity of real planktonic ecosystems. Our general conclusion is that although the functional response of herbivores often does not exist in real ecosystems (especially in the form observed in the laboratory), this framework can be rather useful in modelling - but it does need some amendment which can be made based on various techniques of model reduction. We also show that the shape of the functional response depends on the spatial resolution ('frame') of the model. We argue that incorporating foraging behaviour and spatial heterogeneity in plankton models would not necessarily require the use of individual based modelling - an approach which is now becoming dominant in the literature. Finally, we list concrete future directions and challenges and emphasize the importance of a closer collaboration between plankton biologists and modellers in order to make further progress towards better descriptions of zooplankton grazing.