  The paper is a brief informal introduction to C*-algebraic foundations of
causal contextual subquantum theories. In particular, it is explained how the
contextuality property (which is a necessary consistency condition of all
causal subquantum theories) naturally appears within the framework of certain
C*-algebraic extensions of the quantum observables algebras. Furthermore, a
question of locality is discussed. It is explained that the appropriate
non-Kolmogorovian probability theory allows us to unify both locality and
causality with the principles of quantum mechanics, overcoming the obstacles
given by Bell's inequalities.
