AbstractThis article presents a talk given at 23rd International Conference on Theoretical Physics (Ustroń, 2008). A new version of Bell's theorem is presented, with inequalities based on four assumptions: realism, locality and “free will” and “principle of rotational symmetry of physical laws”. The new Bell‐type inequalities are derived using a simple geometrical intuition. The assumptions behind Bell's theorem are discussed. A critique of overinterpretations of violations of Bell inequalities is given. Further on, a new criterion for entanglement is presented, based on simple geometrical ideas. This leads to a new class of entanglement identifiers, which is richer than entanglement witnesses. Finally a link between Bell's theorem and communication complexity problems will be shown. It covers also realizations, which do not involve entanglement (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)