Although most microwave absorbing materials (MAMs) have good absorption ability above 8 GHz, they perform poorly in the low-frequency range (1–8 GHz). Metal–organic frameworks (MOFs) derived carbon-based composites have been highly sought after in electromagnetic materials and functional devices, due to their high specific area, high porosity, high thermal stability, low reflection loss, and adjustable composition. In this review, we first introduce the three loss types of MAMs and argue that composite materials are effective ways to achieve broadband absorption. Secondly, the absorbing properties of traditional materials and MOF materials in the literature are compared, followed by a discussion of the promising strategies for designing MAMs with broadband absorption in low frequencies based on the recent progress. Finally, the main problems, fabrication methods, and applications are discussed for their future prospects.