We show that a coherent network of lasers exhibits emergent neural computing capabilities. The proposed scheme is built on harnessing the collective behavior of laser networks for storing a number of phase patterns as stable fixed points of the governing dynamical equations and retrieving such patterns through proper excitation conditions, thus exhibiting an associative memory property. The associative memory functionality is first discussed in the strong pumping regime of a network of passive dissipatively coupled lasers which simulate the classical XY model. It is discussed that despite the large storage capacity of the network, the large overlap between fixed-point patterns effectively limits pattern retrieval to only two images. Next, we show that this restriction can be uplifted by using nonreciprocal coupling between lasers and this allows for utilizing a large storage capacity. This work opens new possibilities for neural computation with coherent laser networks as novel analog processors. In addition, the underlying dynamical model discussed here suggests a novel energy-based recurrent neural network that handles continuous data as opposed to Hopfield networks and Boltzmann machines which are intrinsically binary systems.