Hydrogen plays a key role in the transition to a carbon-free economy. One of the areas of hydrogen use is the substitution of hydrocarbon fuel in gas turbine engines and power plants. This review article discusses the features of hydrogen combustion and their influence on the characteristics of combustion chambers in comparison with methane. The paper presents both the results of a study of pure hydrogen or methane and methane-hydrogen mixtures with different hydrogen content. Among the main features, it is worth noting a smaller ignition delay time and higher laminar flame speed with a shift in its maximum value to a rich mixture, which significantly affects on flashback inside burners premixer, especially at elevated air temperatures. Another feature is the increased temperature of the flame, which can lead to an increase in the rate of nitrogen oxides formation. However, wider combustion concentration ranges contribute to the stable combustion of hydrogen at temperatures lower than those of methane. Along with this, it was shown that even at the same adiabatic temperature, more nitrogen oxides are formed in a hydrogen flame than in a methane flame, which indicates an additional mechanism for NOx formation in addition to the Zeldovich mechanism. The article also summarizes some of the results of a study on the effect of hydrogen on the occurrence of thermoacoustic instability, which depends on the initial nature of pulsations during methane combustion. The presented data will be useful both to engineers who are engaged in solving the problems of designing hydrogen combustion devices, and to scientists in this field of study.