Abstract: Metal-organic frameworks (MOFs) are a class of organic–inorganic hybrid functional materials that are generally formed via the self-assembly of metal ions or metal clusters and rigid organic ligands with nitrogen and oxygen atoms. A wide range of potential applications for MOF materials includes gas storage and separation, catalysis, sensing, and drug transportation and release, which is attributable to their versatile designable structures, modifiable chemical functionality, low-density frameworks, large specific surface areas, and functional and permanent pore space. In the past decade, MOFs and their composite materials have also been employed to remove various contaminants from the environment. This paper presented the significant research progress and outcomes achieved using MOF materials in the removal of environmental pollutants from water, based on a review of related studies regarding the removal of heavy metals and organic pollutants from water environments. This represented the first part of a larger paper in which the progress of MOF materials research was presented with respect to the removal of heavy metals from aqueous solution. The presence of heavy metals in water is a global environmental issue that has been receiving considerable attention worldwide. According to previous research reports, MOF materials have high adsorption capacities for common heavy metals, such as Pb²⁺, Cu²⁺, Cd²⁺, Co²⁺, Ag⁺, Cs⁺, Sr²⁺, Hg(II), \rmTcO_4^ - , Se(VI), As(III), and As(V). Some MOF materials have even higher adsorption capacities than conventional adsorbent materials. The adsorption mechanism mainly involves electrostatic attraction, coordination/chelation, ion exchange, and pore adsorption (physical adsorption). Based on a review of previous studies, it is believed that the future research field includes but is not limited to the following: (1) the structure–activity relationship between the MOF structure and heavy-metal removal, (2) the functionalization, surface modification, and pore size adjustment technology of MOF, or the preparation of composite MOF materials, (3) further study of the regulation of the defect structures of MOFs to develop new MOF materials with higher adsorption efficiency, (4) improving the recyclability of MOF materials, and (5) developing new MOF materials with high structural stability, high adsorption capacities, high selectivity, low cost, and which are easily reused.