Coherent systems need carrier phase information at the receiver and they use matched filters (or correlation receiver) to detect and decide what data was sent , while noncoherent systems do not need carrier phase information and use methods like square law (push detection or energy detection) to recover the data.
It's evident that coherent systems need synchronization algorithms to synchronize the local osc. with the transmitter osc. and hence they require more complexity and costs .
In terms of performance coherent systems are much better than noncoherent systems.
regards