This article presents: a talk given at 23rd International Confer-ence on Theoretical Physics (Ustron, 2008). A new version of Bell's theorem is presented, with inequalities based on four as-sumptions: realism, locality and "free will" and " principle ofrotational symmetry of physical laws". The new Bell-type in-equalities are derived using a simple geometrical intuition. Theassumptions 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, basedon simple geometrical ideas. This leads ,to a new class of en-tanglement identifiers, which is richer than entanglement wit-nesses. Finally a link between Bell's theorem and communica-tion complexity problems will be shown. It covers also realiza-tions, which do not involve entanglement.
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