We review experimental and theoretical results on the computing properties of single spiking micropillar lasers and present numerical studies of propagation and computing in chains of evanescently coupled micropillar lasers. Single micropillar lasers are shown to behave as ultrafast optical neurons with sub-nanosecond spike times. They also possess absolute and relative refractory times, spike latency, and show temporal summation. With delayed optical feedback, they emulate an autapse. These basic neural properties can be used for simple photonic computing. We show by numerical simulations of a chain of coupled spiking micropillar lasers that basic logical operations can be implemented in photonic circuits, as well as temporal pattern recognition based on the collision properties of pulses in this chain.