This talk explores neuromorphic computing, an emerging field at the intersection of computational neuroscience and hardware design, focusing on the potential of using stochastic relaxation in recurrent spiking neural networks to efficiently solve combinatorial optimization problems on state-of-the-art neuromorphic chips. We explore the connection between spiking neural networks and the Ising Model, detailing how optimization problems can be mapped to the energy landscape's ground states and how annealing can be used for stochastic relaxation. Integrating these components introduces challenges, particularly the misalignment of neuronal dynamics and ineffective noise generation. We propose to address them by resorting to chaotic networks and a more bio-plausible neural sampling approach.