It has been almost 45 years since the first chemical simulation of the chemistry of dense interstellar clouds was published. This simulation involved 100 gas-phase reactions between 35 molecules with up to 5 atoms. The gas phase was assumed to homogeneous and time-independent. Since that time, astrochemical modelling has become far more detailed, with networks of many thousands of chemical reactions involving both the gas phase and dust surfaces, and thermal and non-thermal physical processes involving the exchange of molecules between the two phases. Moreover, models with heterogeneous conditions, such as those treating photon-dominated regions and protoplanetary disks, have become common, and time-dependence of the physical conditions in the formation of disks and other objects included with approaches that vary in complexity from semi-empirical methods to full three-dimensional magneto-hydrodynamical treatments. The enlargement of chemical networks has been helped by both experimental and theoretical treatments of reaction rate coefficients in both the gas and on dust particles or the mantles that surround them. Sensitivity methods have been employed to determine which reactions are most important to understand better. For a time it was thought that chemical simulations of cold interstellar cloud cores were so accurate as to be predictive, but the detection of more saturated "complex" organic molecules, previously thought to exist only in hot cores, in the gas phase of these objects has complicated matters and led to more complex treatments of the formation of such species, involving both gas and dust. Indeed, new and improved treatments of surface reactions have led to a transformation of this subject, while the inclusion of processes involving tunneling and radiative association has similarly transformed the use of gas-phase chemistry. Although chemical simulations are normally treated by solutions of kinetic rate equations, such treatments are only approximate because of the small number of reactive species per dust particle. More detailed stochastic treatments, involving master equations or Monte Carlo simulations of master equations, are more accurate, but still very computer intensive. Chemical simulations currently exist for all evolutionary periods in the formation of low-mass stars and planets (diffuse clouds, translucent clouds, cold cores, pre-stellar cores, hot corinos, winds, shocks, protoplanetary disks, and even planetary atmospheres, with the simulations for high-temperature regions such as hot corinos the most problematical. In the talk, both the history of astrochemical modeling, and the current level of the subject will be discussed.