This chapter focuses on the physical basis of some integrable spin models in condensed matter physics and the useful physical insights derived from the solution of these models. The antiferromagnetic ground state serves as the physical vacuum for the creation of elementary excitations. The study of integrable models constitutes an important area of theoretical physics. Integrable models in condensed matter physics describe interacting many-particle systems. The most prominent examples are interacting spin and electron systems which include several real materials of interest. Integrable models, because of their exact solvability, provide a complete and unambiguous understanding of the variety of phenomena exhibited by real systems. Integrable models are sometimes more general than what is necessary to describe real systems. A major portion of the review is devoted to physical systems which exhibit rich phenomena, like the systems with both spin and orbital degrees of freedom and undoped and doped spin ladder systems, where the need for integrable systems is particularly strong.