  The aim of this review is to highlight the possibility to apply the
mathematical formalism and methodology of quantum theory to model behaviour of
complex biosystems, from genomes and proteins to animals, humans, ecological
and social systems. Such models are known as quantum-like and they should be
distinguished from genuine quantum physical modeling of biological phenomena.
One of the distinguishing features of quantum-like models is their
applicability to macroscopic biosystems, or to be more precise, to information
processing in them. Quantum-like modeling has the base in quantum information
theory and it can be considered as one of the fruits of the quantum information
revolution. Since any isolated biosystem is dead, modeling of biological as
well as mental processes should be based on theory of open systems in its most
general form -- theory of open quantum systems. In this review we advertise its
applications to biology and cognition, especially theory of quantum instruments
and quantum master equation. We mention the possible interpretations of the
basic entities of quantum-like models with special interest to QBism is as may
be the most useful interpretation.
