Theoretical chemists have always strived to perform quantum mechanics (QM) calculations on larger and larger molecules and molecular systems, as well as condensed phase species, that are frequently much larger than the current state-of-the-art would suggest is possible. The desire to study species (with acceptable accuracy) that are larger than appears to be feasible has naturally led to the development of novel methods, including semiempirical approaches, reduced scaling methods, and fragmentation methods. The focus of the present review is on fragmentation methods, in which a large molecule or molecular system is made more computationally tractable by explicitly considering only one part (fragment) of the whole in any particular calculation. If one can divide a species of interest into fragments, employ some level of ab initio QM to calculate the wave function, energy, and properties of each fragment, and then combine the results from the fragment calculations to predict the same properties for the whole, the possibility exists that the accuracy of the outcome can approach that which would be obtained from a full (nonfragmented) calculation. It is this goal that drives the development of fragmentation methods.