Context. The microlensing of stars in our Galaxy has long been used to detect and characterize stellar populations, exoplanets, brown dwarfs, stellar remnants, and all other objects that may magnify the source stars with their gravitational fields. The interpretation of microlensing light curves is relatively simple for single lenses and single sources, but it becomes more and more complicated when we add more objects and take their relative motions into account. Aims. RTModel is a modeling platform that has been very active in the real-time investigations of microlensing events, providing preliminary models that have proven very useful for driving follow-up resources towards the most interesting events. The success of RTModel comes from its ability to carry out a thorough and focused exploration of the parameter space in a relatively short time. Methods. This modeling process is based on three key ideas. First, the initial conditions are chosen from a template library including all possible caustic crossing and approaches. The fits are then made using the Levenberg-Marquardt algorithm with the addition of a bumper mechanism to explore multiple minima. Finally, the basic computations of microlensing magnification are performed by the fast and robust VBBinaryLensing package. Results. In this paper, we illustrate all the algorithms of RTModel in detail with the intention to foster new approaches in view of future microlensing pipelines aimed at massive microlensing analyses.