Water covers about 70% of the Earth’s surface, but the amount of freshwater available for human use is only 2.5% and, although it is continuously replenished via the water cycle, freshwater is a finite and limited resource. The Earth’s water is affected by pollution and while water quality is an issue of global concern, the specific regulations on contaminants of emerging concern (CECs) are limited. In order to achieve the goals set by EU regulations, the treatment of wastewater is a scientifically and technologically challenging issue. Metal–organic frameworks (MOFs) are promising materials used for the removal of priority and emerging contaminants from wastewater, since they can mitigate those contaminants via both adsorption as well as catalysis processes. MOFs can offer selective adsorption of CECs by various adsorption mechanisms. The catalytic removal of priority and emerging organic contaminants from wastewater using MOFs implies Fenton, electro-Fenton, and photo-Fenton processes. Overall, MOFs can be considered as promising materials for the elimination of priority and emerging organic contaminants from various wastewater types, but the involved processes must be studied in detail for a larger number of compounds.