The present paper reports some new approaches to describing the collective behaviour of complex systems in mathematical biology based on evolution equations of observables of an open system. This framework of kinetic evolution seems to be the most direct and mathematically fully consistent formulation that models collective behaviour, whereas the traditionally used concept of state in kinetic theory is more subtle and is an implicit characteristic of populations of living creatures. An advantage of the developed approach is the possibility of constructing kinetic equations for the open complex systems in large-scale approximations involving initial correlations, which can characterise condensed states of active soft matter. The approach is also related to the challenging problem of getting a rigorous derivation of the non-Markovian kinetic equations from underlying many-entity dynamics, which makes it possible to describe the memory effects of the collective behaviour of living creatures.