We consider generic properties of conic programs like SDPs and copositive programs. In this context, a property is called generic, if it holds for ``almost all" problem instances. Genericity of properties like non-degeneracy and strict complementarity of solutions has been studied before. In this talk, we discuss genericity of Slater's condition in conic programs. We also discuss the order of the solutions in SDP and copositive problems, which has important consequences for the convergence rate in discretization methods.