Abstract: Jupiter and Saturn, as the gas giants of our solar system, account for over 90% of the total mass beyond the Sun and hold most of the system's angular momentum, playing a crucial role in the early history of the solar system. During their formation, these planets captured vast amounts of material from the protoplanetary disk. Their internal structure and interior composition are fundamentally affected by material interaction, gravitational collapse, and subsequent long-term thermal evolution. Exploring the interior structure of the gas giants provides critical insights into several core questions in planetary sciences, including the conditions and evolutionary history of the protosolar nebula, the formation and evolution mechanisms of solar system planets, and the interior structure and evolution history of giant exoplanets. Furthermore, comparative studies between Jupiter and Saturn reveal important differences in their internal dynamics and evolutionary pathways, offering valuable benchmarks for understanding giant planets both within and beyond our solar system. Current research on the interior structure of the gas giants primarily relies on external observational constraints such as gravity fields, magnetic fields, and atmospheric properties. However, inferring the interior structure from these constraints is inherently a highly degenerate inversion problem, depending on interior structural models, internal material properties, and calculations of planetary shape and gravity fields. Modern approaches increasingly integrate multiple physical constraints by combining gravity harmonics with magnetic field measurements and zonal wind profiles to reduce degeneracies in interior models. In recent years, the Juno and Cassini spacecraft have conducted close orbital explorations of Jupiter and Saturn, respectively, acquiring unprecedented high-precision gravity field data. Simultaneously, experimental and theoretical research on the physical properties of hydrogen and helium under extreme temperature and pressure conditions has achieved critical breakthroughs. With these in mind, this paper reviews the major exploration missions for Jupiter and Saturn and elaborates on the core aspects of interior modelling, such as theoretical calculations of planetary shapes and gravity fields, current knowledge of hydrogen/helium microphysical properties. The research progress on the internal structures of Jupiter and Saturn is also summarized, showing some representative frontier achievements.