The lattice Boltzmann method, after close to thirty years of presence in computational fluid dynamics has turned into a versatile, efficient and quite popular numerical tool for fluid flow simulations. The lattice Boltzmann method owes its popularity in the past decade to its efficiency, low numerical dissipation and simplicity of its algorithm. Progress in recent years has opened the door for yet another very challenging area of application: Combustion simulations. Combustion is known to be a challenge for numerical tools due to, among many others, the large number of variables and scales both in time and space, leading to a stiff multi-scale problem. In the present work we present a comprehensive overview of models and strategies developed in the past years to model combustion with the lattice Boltzmann method and discuss some of the most recent applications, remaining challenges and prospects.