I will present recent results in modeling predator's behaviour based on optimal foraging theory. The mortality operator that can be derived from these considerations has a number of 'good' properties that are missing for Holing type functional response. I will show that one of the straightforward consequences of optimal foraging is the stability of population equation N' = bN - m(N)*M, where N is the density of prey, m(·) is the mortality operator, b is the birth rate and M is a constant predator density. Introducing size structure leads to other interesting conclusions about selectivity of the predator and the stationary size distribution of the prey. Finally, I will speak about computational challenges I have come across during my research on optimal foraging.