We have experimentally investigated the soliton interaction in a passively mode-locked fiber ring laser and revealed the existence of three types of strong soliton interaction: a global type of soliton interaction caused by the existence of unstable cw components, a local type of soliton interaction mediated through the radiative dispersive waves, and the direct soliton interaction. We found that the appearance of the various soliton operation modes observed in the passively mode-locked fiber soliton lasers are the direct consequences of these three types of soliton interactions. The soliton interaction in the laser is further numerically simulated based on a pulse tracing technique. The numerical simulations confirmed the existence of the dispersive-wave-mediated soliton interaction and the direct soliton interaction. Furthermore, it was shown that the resonant dispersive-wave-mediated soliton interaction in the laser always has the consequence of causing random irregular relative soliton movement and the experimentally observed states of bound solitons are caused by the direct soliton interaction. In particular, as the solitons generated in the laser could have a profile with long tails, the direct soliton interaction could extend to a soliton separation that is larger than 5 times the soliton pulse width.