Transient stability (TS) and electromagnetic transient (EMT)programs are widely used simulation tools in power systems, with distinct applications but competing requirements. TS programs are fast which makes them suitable for handling large-scale networks, however, the modeling is not sufficiently detailed. On the other hand, EMT simulators are highly detailed, but limited in speed; consequently, they are used to simulate only small portions of the network. Integrating these two types of simulators generates a hybrid simulator which inherits the merits of both programs. A hybrid simulator can fulfill the modeling requirements of a large network by providing a fast as well as a detailed simulation. Establishing a connection between two different programs brings up several important issues which have been addressed, classified, and explained in this paper. An alternative integrated modeling of TS and EMT is also discussed using the concept of frequency shifting.