Oil contaminated water is a global issue, decreasing the quality of water sources and is posing a threat to the health of humans and many ecosystems. The utilization of industrial level strategies is limited mainly due to their complex and time-consuming processing. Considering this, we choose materials for separating oils from water based on their ease of handling and good performance. However, high surface area porous materials, such as linens, zeolites, cotton, etc., offer low efficiency for oil/water separation. Special wettability is the most promising property of materials and is helpful for oil-water separation. Metal-organic frameworks (MOFs), a class of highly tunable porous structures of metal clusters/ions and multidentate organic ligands, offer exciting prospects for various applications. The unique tunability of the structure and properties of these materials can endow them with special wettability for the treatment of oily water. This review focuses on hydrophobic-oleophilic, hydrophilic-underwater oleophobic and switchable wettability MOFs and their implementation as oil/water separating materials. We classify different MOF-based materials as filtration materials, absorbents or adsorbents based on the methodology they are used in for separating oil/water mixtures and emulsions. We discuss different subclasses of MOF-based filtration, absorbent and adsorbent materials and summarize recent developments in their oil/water separation applications. Finally, we end our discussion by critically analyzing the importance of these MOFs for separating oils from water and highlighting potential future directions for achieving improved performance.