The objective of this paper is to review the progress made in understanding the effects of fuel composition on premixed gas turbine combustion, with a special emphasis on system stability and emissions, for hydrogen-rich synthetic gas (syngas) mixtures. This is driven by the rising interest in the use of hydrogen blends and syngas in combined cycle power plants, as an alternative to standard natural gas. Typical applications where such mixtures are used include the recycling of hydrogen by-product from industry as well as promising pre-combustion carbon capture methods like fuel reforming or gasification integrated with gas turbine combined cycle plants. Syngas is mainly a mixture of H2, CO and CH4; its composition can vary due to fluctuations in the process’s conditions but can also dramatically change if the feedstock is modified like coal or biomass grades in gasification. Due to the substantially different chemical, transport and thermal properties that distinguish the syngas components, especially H2, when compared with conventional hydrocarbon fuels, these non-standard fuels pose several challenges in premixed combustion. These challenges are reviewed in this paper along with the combustion fundamentals of these fuels. A survey of available technologies able to handle syngas and hydrogen-rich fuel in general is provided reflecting the difficulties encountered while using these fuels in real large scale commercial applications. We find that a limited number of options exist today for fully premixed combustion, but promising designs are under development. Finally, the ever growing use of numerical simulation to cost-effectively study full scale combustion systems—with Large Eddy Simulations (LES) being at the forefront as a compromise between accuracy and computational cost—justifies the simultaneous review of the different numerical attempts to simulate hydrogen-containing fuel mixtures and syngas in premixed combustion. Challenges specific to performing LES calculations for these reacting flows are highlighted. We find that, while the literature on premixed LES methane combustion is abundant, LES of premixed syngas and hydrogen-rich fuels combustion is comparatively scarce. Only few attempts were made so far showing the need for more research effort in this area to help tackle the challenges presented by these fuels.