Abstract: Recent years were characterized by an increasing of interest for applications of the mathematical formalism of quantum theory and its methodology to information processing and human choice behaviour in cognition, decision making, artificial intelligence, economics and finance and also social and political science. Contextual expectations and choices in real economic and financial decision making settings, non-neutral attitudes to ambiguity and problems of complete nonknowledge are posing a challenge to standard decision theories that utilize the calculus of classical probability theory. A new area that showed a potential to cope with the non-classical decision making statistics of humans is known as quantum-like modeling. Its basic tool is quantum calculus of probabilities, which is based on operation with complex probability amplitudes and the usage of Born’s rule to convert complex probability amplitudes into objective probabilities. In this paper we expose a brief review introducing the core axiomatic differences between classical and quantum probability as well as discuss the decision-making settings in which quantum probability can capture agents’ non-classical beliefs, superposition of ambiguous economic and financial events, and other instances of non-classical information processing.