The aim of this chapter is to highlight the possibility of applying the mathematicalformalism and methodology of quantum theory to model behaviourof complex biosystems, from genomes and proteins to animals, humans, ecologicaland social systems. Such models are known as quantum-like and theyshould be distinguished from genuine quantum physical modeling of biologicalphenomena. One of the distinguishing features of quantum-like models istheir applicability to macroscopic biosystems, or to be more precise, to informationprocessing in them. Quantum-like modeling has the base in quantuminformation theory and it can be considered as one of the fruits of the quantuminformation revolution. Since any isolated biosystem is dead, modelingof biological as well as mental processes should be based on theory of opensystems in its most general form – theory of open quantum systems. In thischapter we advertise its applications to biology and cognition, especiallytheory of quantum instruments and quantum master equation. We mentionthe possible interpretations of the basic entities of quantum-like models withspecial interest to QBism as maybe the most useful interpretation.