Covalent organic frameworks comprise a unique class of functional materials that has recently emerged as a versatile tool for energy-related, photocatalytic, environmental, and electrochromic device applications. A plethora of structures can be designed and implemented through a careful selection of ligands and functional units. On the other hand, porous materials for heavy metal absorption are constantly on the forefront of materials science due to the significant health issues that arise from the release of the latter to aquatic environments. In this critical review, we provide insights on the correlation between the structure of functional covalent organic frameworks and their heavy metal absorption. The elements we selected were Pb, Hg, Cr, Cd, and As metal ions, as well as radioactive elements, and we focused on their removal with functional networks. Finally, we outline their advantages and disadvantages compared to other competitive systems such as zeolites and metal organic frameworks (MOFs), we analyze the potential drawbacks for industrial scale applications, and we provide our outlook on the future of this emerging field.