The utilization of fossil fuels is currently transforming to low-carbon or zero-carbon fuels, which is one of the solutions to global warming. Hydrogen and ammonia are regarded as promising zero-carbon fuels in power supply and transportation scenarios but the availability of hydrogen and their distinctly different chemical activity constrain their large-scale direct utilizations. Fuel blends with physical and chemical complementary are considered as the effective approaches in the utilization of hydrogen and ammonia because no significant modification to the existing end-user infrastructures is needed. This paper reports recent progress in the fundamental combustion behaviors of fuel blends, focusing on hydrogen-hydrocarbon blends and ammonia-hydrocarbon blends. Firstly, laminar flame behaviors, auto- and forced-ignition characteristics, and pollutant emissions of binary fuels containing hydrogen are reviewed, all of which are supplemented with a discussion on the governing hydrogen-enriched combustion chemistry. Subsequently, the hydrogen-enriched flame responses to the flow conditions are discussed, including the turbulent burning velocity and statistical structures, the flashback swirl flames, thermoacoustic instabilities, and the jet ignition characteristics; Furthermore, with the increasing concern over ammonia as a zero carbon fuel and its extremely weak reactivity, recent progress on combustion of fuel blends containing ammonia are also reviewed. The fundamental combustion chemistry studies including laminar burning velocity, the ignition delay times data collection, as well as the attempts for chemical kinetic modeling development for fuel blend with ammonia are presented. The literature reported ammonia containing blends of turbulent flame characteristics are presented. Finally, from an engineering point of view, examples using hydrogen blends in practical internal combustion engines and in gas turbines are introduced, including the topic of engine efficiency performance and pollutant emissions and different combustors for gas turbines. It is suggested that fuel blends with hydrogen or ammonia that potentially monitors the overall reactivity will be one realistic solution to de-carbonization, on the basis of current transportation and power generation systems.