The overarching objective of the present endeavor is to demonstrate the universal character of combustion phenomena for various areas of modern physics, focusing on inertial confinement fusion (ICF) in this review. We present the key features of laser deflagration, and consider the similarities and differences between the laser plasma flow and the slow combustion front. We discuss the linear stage of the Rayleigh-Taylor instability in laser ablation, short-wavelength stabilization of the instability due to the mass flow, and demonstrate the importance of the concepts and methods of combustion science for an understanding of the corresponding ICF processes. We show the possibility of the Darrieus-Landau instability in the laser ablation flow and discuss the specific features of the instability at the linear and nonlinear stages as compared to the combustion counterpart of this phenomenon. We consider the nonlinear stage of the Rayleigh-Taylor instability in the ICF and generation of ultra-high magnetic field by the instability, and show that proper understanding of vorticity production in the laser plasma and, hence, of the magnetic field generation requires concepts from combustion science. (C) 2014 Elsevier Ltd. All rights reserved.