Nonphotochemical hole burning in the absorption spectra of impurity molecules dissolved in amorphous solids has been studied for several impurity-host systems. These systems are divided into four classes according to holeburning occurrence and hole shape. The hole formation mechanism and possible explanations for each class of holes are discussed;Hole burning of tetracene in 3:2:2 glycerol/dimethylsulfoxide/N,N-dimethylformamide was studied as a function of burn temperature (T(,B)), and annealing (hole disappearance) was studied for T > T(,B). Hole widths show that the pure dephasing of the impurity electronic state is orders of magnitude faster than found in crystalline media. This anomalously fast dephasing is explained by a theory considering the excited impurity to interact with two level systems (TLSs) in the host solid which undergo rapid phonon assisted tunneling transitions involving very low frequency phonons. The high temperature limit, where the dephasing frequency is linear in T, occurs in this theory for T(, )<(, )1K, providing an estimate of the width of the distribution function f((epsilon)), where (epsilon) denotes the TLS asymmetry. The relationship between this theory and similar theories for TLS dephasing of fluorescence transitions of rare earth ions in inorganic glasses is discussed. A new interpretation for the fluorescence linewidths of Pr('3+) in inorganic glasses using the theory described here and the two-phonon Raman line broadening theory is given;A new theory is developed to explain the annealing process. TheTLS barrier height is allowed to vary with the order parameter of anorder-disorder transition assumed to be characteristic of amorphoussolids. A constant distribution of critical temperatures based on thedegree of local ordering of the host solid gives a linear intensitydecrease with annealing temperature as observed for thermallyactivated barrier crossings. This theory is shown to be consistent;with the hole formation and dephasing theories and all existing data;('1)DOE Report IS-T-963. This work was performed under contractW-7405-eng-82 with the Department of Energy.