Quantum simulators are controllable quantum systems that can be used to mimic other quantum systems. They have the potential to enable the tackling of problems that are intractable on conventional computers. The photonic quantum technology available today is reaching the stage where significant advantages arise for the simulation of interesting problems in quantum chemistry, quantum biology and solid-state physics. In addition, photonic quantum systems also offer the unique benefit of being mobile over free space and in waveguide structures, which opens new perspectives to the field by enabling the natural investigation of quantum transport phenomena. Here, we review recent progress in the field of photonic quantum simulation, which should break the ground towards the realization of versatile quantum simulators.