Before being detected at Earth, charged cosmic-rays propagate across the Solar System and undergo interactions with the turbulent solar wind and with the heliospheric magnetic field. As a result, they are subject to a series of processes that include diffusion, convection, energy losses and drifts, which significantly affect the shape and the intensity of the cosmic-ray fluxes at low energies. Here we illustrate how all these mechanisms can be realistically modelled with HelioProp, our public tool designed to treat cosmic-ray transport through the heliosphere in a charge-dependent way. We present a detailed description of the features of the code and we illustrate in a quantitative way the effects that the propagation in the heliosphere can have on the different cosmic ray species with a particular emphasis on the antiparticle channels relevant for dark matter indirect detection.