Van der Waals heterostructures consisting of graphene and transition metal dichalcogenides have shown great promise for optoelectronic applications. However, an in-depth understanding of the critical processes for device operation, namely, interfacial charge transfer (CT) and recombination, has so far remained elusive. Here, we investigate these processes in graphene-WS2 heterostructures by complementarily probing the ultrafast terahertz photoconductivity in graphene and the transient absorption dynamics in WS2 following photoexcitation. We observe that separated charges in the heterostructure following CT live extremely long: beyond 1 ns, in contrast to ~1 ps charge separation reported in previous studies. This leads to efficient photogating of graphene. Furthermore, for the CT process across graphene-WS2 interfaces, we find that it occurs via photo-thermionic emission for sub-A-exciton excitations and direct hole transfer from WS2 to the valence band of graphene for above-A-exciton excitations. These findings provide insights to further optimize the performance of optoelectronic devices, in particular photodetection.