Transport models have been very useful in studying the properties of the hot, dense matter that is created in relativistic heavy-ion collisions. We review here a Relativistic Transport (ART) Model and its applications in heavy ion collisions at beam energies below about 10 AGeV available from the Alternating Gradient Synchrotron at Brookhaven National Laboratory. The model allows one to study not only the reaction dynamics leading to the formation of superdense hadronic matter, but also to explore the effects due to the nuclear equation of state and the deformation/orientation of the colliding nuclei on the size and lifetime of the superdense matter. We also discuss the dependence of the central baryon and energy densities, the degree of thermalization, and the collective radial flow velocity of the superdense matter on the beam energy. We further review how the properties of the superdense hadronic matter can be determined from studying the collective flow of nucleons, pions and kaons in these collisions. We finally discuss the mechanisms for kaon production in relativistic heavy-ion collisions and review the progress in extracting the kaon in-medium properties from these collisions.