Organic matter decomposition is a very important process within the Earth System because it controls the rates of mineralization of carbon and other biogeochemical elements, determining their flux to the atmosphere and the hydrosphere. SOILR is a modeling framework that contains a library of functions and tools for modeling soil organic matter decomposition under the R environment for computing. It implements a variety of model structures and tools to represent carbon storage and release from soil organic matter. In SOILR organic matter decomposition is represented as a linear system of ordinary differential equations that generalizes the structure of most compartment-based decomposition models. A variety of functions is also available to represent environmental effects on decomposition rates. This document presents the conceptual basis for the functions implemented in the package. It is complementary to the help pages released with the software.