The removal of contaminants from wastewaters is a major challenge in the field of water pollution. Among numerous techniques available for contaminant removal, adsorption using solid materials, named adsorbents, is a simple, useful and effective process. The adsorbent matter can be mineral, organic or biological. Activated carbon is the preferred, conventional material at the industrial scale. Activated carbon is extensively used not only for removing pollutants from wastewater streams, but also for adsorbing contaminants from drinking water sources, e.g., groundwater, rivers, lakes and reservoirs. However, the widespread use of activated carbon is restricted due to a high cost. In the last three decades, numerous approaches using non-conventional adsorbents have been studied for the development of cheaper and more effective adsorbents to eliminate pollutants at trace levels. This review gives an overview of liquid-solid adsorption processes using conventional and non-conventional adsorbents for pollutant removal. The manuscript outlines the principles of adsorption and proposes a classification for adsorbent materials. Finally, the various mechanisms involved in the adsorption phenomena are discussed.