Limit cycles in continuous and discontinuous piecewise linear differential systems with two pieces separated by a straight line

This paper is a survey on the study of the maximum number of limit cycles of planar continuous and discontinuous piecewise linear differential systems defined in two half–planes separated by a straight line $L$. We restrict our attention to the crossing limit cycles, i.e. to the limit cycles having exactly two points on the straight line $L$. We summarize the results known by now and describe the tools for obtaining them.