Solid fuel combustion produces harmful particulate matter (PM) and gaseous emissions in the flue gas. To mitigate PM, advanced filtration materials using metal meshes, metal composites, and MOF-polymer composites have been studied. Gaseous emissions can be adsorbed using metal-organic frameworks (MOFs). Metal filters are suitable for high-temperature flue gas filtration (>200 °C) thanks to their high mechanical strength and thermal stability. This review covers research articles (2019–2023) on metal filters and MOF-polymer composites for flue gas filtration. While metal filters are already widely implemented in industrial systems, MOF-polymer composites remain at the research and development stage. Particular emphasis is placed on their filtration performance at high-temperature flue gas and assessment of their potential in combustion systems.