We report on ultrafast artificial laser neurons and on their potentials for future neuromorphic (brain-like) photonic information processing systems. We introduce our recent and ongoing activities demonstrating controllable excitation of spiking signals in optical neurons based upon Vertical-Cavity Surface Emitting Lasers (VCSEL-Neurons). These spiking regimes are analogous to those exhibited by biological neurons, but at sub-nanosecond speeds (>7 orders of magnitude faster). We also describe diverse approaches, based on optical or electronic excitation techniques, for the activation/inhibition of sub-ns spiking signals in VCSEL-Neurons. We report our work demonstrating the communication of spiking patterns between VCSEL-Neurons towards future implementations of optical neuromorphic networks. Furthermore, new findings show that VCSEL-Neurons can perform multiple neuro-inspired spike processing tasks. We experimentally demonstrate photonic spiking memory modules using single and mutually-coupled VCSEL-Neurons. Additionally, the ultrafast emulation of neuronal circuits in the retina using VCSEL-Neuron systems is demonstrated experimentally for the first time to our knowledge. Our results are obtained with off-the-shelf VCSELs operating at the telecom wavelengths of 1310 and 1550 nm. This makes our approach fully compatible with current optical network and data centre technologies; hence offering great potentials for future ultrafast neuromorphic laser-neuron networks for new paradigms in brain-inspired computing and Artificial Intelligence.