We present our recent developments on numerical algorithms for computing photon and charged particle trajectories in the surrounding of compact objects. Strong gravity around neutron star and black holes causes relativistic effects on the motion of massive particles and distorts light rays due to gravitational lensing. Fast, efficient numerical methods are required in order to solve the geodesic equation and i) compute the black hole shadow obtained by tracing light rays from the object to a distant observer, ii) obtain information on the dynamics of the plasma at the microscopic scale. Here, we present advanced, generalized algorithms capable of simulating ensembles of photons and massive particles in any 3+1 split spacetime, with the option of including external forces such as the Lorentz force. The coupling of these tools with GRMHD simulations is the key point for obtaining a complete view on the complex dynamics of accretion disks and jets and for comparing simulations with upcoming observational results from the Event Horizon Telescope.