Technologies Intermittent Cutting Problem and Endpoint Cutting Problem for cutting the sheet material belong to so called resource-saving technologies. These technologies allow to overlap the contours of cut-off details. This paper is devoted to review of mathematical models for cut-off (lie details by these technologies and algorithms for defining the cutter route according to some technological restrictions. (C) 2016, IFAC (International Federation of Automatic. Control) Hosting by Elsevier Ltd. All rights reserved.