Significance: With the accelerating pace of human aerospace endeavors and broadening horizons of space exploration, investigating combustion phenomena in variable-gravity environments, particularly microgravity and supergravity, has emerged as a research frontier in aerospace science. Comparing to diffusion flames, premixed flames makes more adequate combustion, which improves energy efficiency and generates much less pollutants. Thus it is essential to elucidate how gravity influences these flames to optimize combustion processes in space. This review aims to consolidate current knowledge on gravity's effect on premixed jet flames, fostering advancements in aerospace combustion technology. Progress: This article systematically surveys domestic and international research advancements on how gravity affects premixed jet flames. It encompasses various experimental setups designed to simulate microgravity and supergravity conditions, including tower drop experiments, centrifuge facilities, and aircraft weightlessness simulations. The focus is on various flame configurations, such as conical, rod-stabilized, and polyhedral jet flames. The effects of gravity on flame morphology, stability, flickering behavior are examined using multiple techniques such as laser imaging for flame visualization, particle image velocimetry for flow field measurements, planar-laser-induced fluorescence for species-concentration mapping, and computational fluid dynamics simulations for detailed mechanistic insights. These methodologies help explore the complex interactions among fluid dynamics, heat transfer, and chemical kinetics under altered-gravity conditions. Furthermore, the review examines different control parameters, such as the equivalence ratio, Reynolds number, and initial pressure, which influence the behavior of premixed flames. Attention is also given to experimental conditions that affect the reproducibility and generalizability of the findings, such as fuel type, combustion-chamber geometry, and specific flame initiation and stabilization procedures. The findings reveal that gravity significantly affects the characteristics of premixed jet flames, influencing their shape, stability, and dynamic behavior. In terms of flame shape, the review demonstrates how gravity significantly influences the geometric structure. Microgravity causes flames to become more spherical owing to reduced buoyancy effects, while supergravity elongates and distorts flames owing to intensified buoyancy-driven flows. In terms of flame stability, the stability boundaries of premixed flames are found to be highly dependent on the magnitude of gravity. Microgravity allows for a broader range of stable operations, while supergravity narrows these boundaries, leading to increased instability and flame extinguishment. The review also addresses buoyancy-induced flame flickering, highlighting that the flickering frequency is directly related to the magnitude of gravity. Lower gravity magnitudes lead to less frequent flickering owing to diminished buoyancy-induced shear-layer oscillations. Conversely, increased gravity magnitudes intensify these oscillations, increasing the flickering frequency. Conclusions and Prospects: This comprehensive review consolidates state-of-the-art knowledge on the effect of gravity on premixed jet flames, offering valuable insights for researchers. It underscores the significance of ongoing exploration in the aerospace domain, driven by advancements in experimental techniques and computational modeling. By providing theoretical underpinnings and practical guidance, this review aims to stimulate further research, driving the development of more efficient and environmentally friendly space propulsion systems.