The bleaching process with activated clays in the edible‐oil industry is a combination of catalytic action (i.e. peroxide destruction) and equilibrium adsorption (i.e. pigment removal). However, the removal of particular noncolored constituents during bleaching is necessary also if high‐quality oil is to be produced. Four key aspects are addressed: (i) the use of adsorptive purification agents (activated carbon, bleaching earth, and silica hydrogel), (ii) the adsorptive removal of targeted constituents, (iii) practical means and methods to achieve optimal bleaching efficiency and efficacy, and (iv) approaches for dealing with spent adsorbents, including utilization/disposal, and best methods to recover retained oils. The future trends on bleaching for the oil industry point out to develop more cost‐efficient process designed for processing a wide range of different oils, reduce the by‐products, and considering larger bleaching facilities to take advantage of scale economies. Additionally, in accordance with the consumer trend to consume healthier and natural foods, there is a need to develop innovative bleaching processes that enhance the presence of several native oil/fat components.