Access to drinkable water is becoming more and more challenging due to worldwide pollution and the cost of water treatments. Water and wastewater treatment by adsorption on solid materials is usually cheap and effective in removing contaminants, yet classical adsorbents are not sustainable because they are derived from fossil fuels, and they can induce secondary pollution. Therefore, biological sorbents made of modern biomass are increasingly studied as promising alternatives. Indeed, such biosorbents utilize biological waste that would otherwise pollute water systems, and they promote the circular economy. Here we review biosorbents, magnetic sorbents, and other cost-effective sorbents with emphasis on preparation methods, adsorbents types, adsorption mechanisms, and regeneration of spent adsorbents. Biosorbents are prepared from a wide range of materials, including wood, bacteria, algae, herbaceous materials, agricultural waste, and animal waste. Commonly removed contaminants comprise dyes, heavy metals, radionuclides, pharmaceuticals, and personal care products. Preparation methods include coprecipitation, thermal decomposition, microwave irradiation, chemical reduction, micro-emulsion, and arc discharge. Adsorbents can be classified into activated carbon, biochar, lignocellulosic waste, clays, zeolites, peat, and humic soils. We detail adsorption isotherms and kinetics. Regeneration methods comprise thermal and chemical regeneration and supercritical fluid desorption. We also discuss exhausted adsorbent management and disposal. We found that agro-waste biosorbents can remove up to 68–100% of dyes, while wooden, herbaceous, bacterial, and marine-based biosorbents can remove up to 55–99% of heavy metals. Animal waste-based biosorbents can remove 1–99% of heavy metals. The average removal efficiency of modified biosorbents is around 90–95%, but some treatments, such as cross-linked beads, may negatively affect their efficiency.