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We introduce the notion of a boxed mesh pattern and study avoidance of these patterns on permutations. We prove that the celebrated former Stanley-Wilf conjecture is not true for all but eleven boxed mesh patterns; for seven out of the eleven patterns the former conjecture is true, while we do not know the answer for the remaining four (length-four) patterns. Moreover, we prove that an analogue of a well-known theorem of Erdős and Szekeres does not hold for boxed mesh patterns of lengths largerdoi:10.1016/j.dam.2012.08.015 fatcat:gsdyihucfzetnky4trw647nkfm