Basically, there are two ways to simulate the behavior of a system: either one can describe its evolution analytically, in which case computers are used to find the solution of the dynamic equations, or a probabilistic approach is used, in which at each step pseudo-random numbers are used to select one among different physics processes. Examples of the first approach are the computation of space probe trajectories in the solar system and of charged particle paths inside a magnetic field. When dealing with the interactions of particles with matter, the second approach is usually followed, because of the variety of possible physics processes and of their discrete nature. Because such approach is based on pseudo-random numbers, it is usually called a "Monte Carlo" method, dreaming about winning money in the casino...

TVirtualMC provides a virtual interface to Monte Carlo applications, allowing the user to build a simulation independent of any actual underlying Monte Carlo implementation itself. A user will have to implement a class derived from the abstract Monte Carlo application class, and provide functions like ConstructGeometry(), BeginEvent(), FinishEvent(), ... The concrete Monte Carlo implementation (Geant3, Geant4, Fluka) is selected at run time - when processing a ROOT macro where the concrete Monte Carlo object is instantiated. This allows for comparison between different engines (necessary to estimate the theoretical uncertainties) using a single application.

Monte Carlo simulations always have to describe the input particles, together with their interactions, and the detector (geometry, materials and read-out electronics). The definition of particles, available interactions and detector is carried on during the initialization phase. The main body of the application is then a loop over all particles, that are traced through all materials until they exit, stop or disappear (by decay or annihilation). The tracing is done in a discrete fashion: at each step, the detector volume is found in which the particle is located and pseudo-random numbers are used to "draw" one among possibly several physical processes, to simulate the interaction of the particle with the matter. If an interaction occurs, the energy lost by the particle is computed (again, it is usually a random process) and subtracted from its kinetic energy. When the latter reaches zero, the particle stops in such volume, otherwise a new step is performed.

Having computed the energy lost by all particles inside the detector, one has to simulate the behavior of the read-out electronics. This is usually done later, with another program that receives the energy lost in different locations as input, but it can also be done by the very same application that is performing the particle tracing inside the detector. Usually, the simulation of the read-out electronics also involves some use of pseudo-random generators, at least to simulate the finite resolution of any real measuring device.