In this paper we study the class of orthogonal ray graphs (ORGs). An ORG is the intersection graph of axis-parallel rays. We distinguish two subclasses of ORG, which limit the directions for the rays to two (2DORG) or three (3DORG) directions. There are several characterizations for 2DORGs and a polynomial-time recognition algorithm. We achieve some results towards a similar characterization for 3DORGs.
Afterwards, we look at some well-known combinatorial problems (e.g., MIS and FVS), which are NP-hard on general graphs. We can solve these problems in polynomial times on ORGs and also give specialized algorithms for 2DORGs and 3DORGs.