The particular role played by the exchange interaction modulated by lattice vibrations ͑phonons͒ in effecting spin-lattice relaxation in amorphous materials in conjunction with the spin-orbit coupling, along with the role played by the well-known mechanisms, such as coupling to tunneling level states ͑TLS͒ via dipolar and Fermi-contact hyperfine interactions, is investigated. From a review of experimental data, it is found that the relaxation rate as effected by the exchange interaction is two to three orders of magnitude faster than that due to coupling with TLS centers. In particular, it is deduced that both the exchange interaction and coupling to TLS centers via Fermi-contact hyperfine, or electron-nuclear dipolar interaction, lead, in general, to a quadratic temperature dependency of the relaxation rate at low temperatures changing into a linear temperature dependency at intermediate temperatures. However, when the exchange interaction is strong, the relaxation rate becomes independent of temperature at higher temperatures due to cross relaxation of a spin with an exchangecoupled pair of spins, coupled to it via the exchange interaction. This analysis is then applied to interpret the spin-lattice relaxation data on ͑i͒ Cr 3ϩ ions in the Cu 2ϩx Cr 2x Sn 2Ϫ2x spinel samples for xϭ0.1 and 0.2 in the semiconductor range (xр0.5), and ͑ii͒ dangling bonds, with spin 1 2 , in amorphous silicon.