Laser absorption spectroscopy (LAS) has been rapidly developed and widely applied to combustion diagnosis in recent decades. As a cost-effective tool for measuring multiple combustion parameters, LAS provides unique properties in terms of accuracy and sensitivity for understanding the reactions and kinetics in reactive flows. Line-of-sight and tomographic LAS techniques have stimulated numerous applications and been proved to be robust for in situ combustion diagnosis in uniform and non-uniform combustion fields, respectively. This review highlights the breakthroughs in the evolution of LAS techniques from the viewpoints of key principles, sensors and instrumentations developed for combustion diagnosis, with particular emphasis on a series of spatially-resolved LAS techniques with their recent applications on obtaining high-fidelity measurement results with minimal intrusion to the practical combustors. Along the way, we note some challenges and requirements for further development of the LAS-based combustion diagnosis.