Micro- and nanoplastics are emerging contaminants of international concern that cannot be ignored as future environmental threats. New studies are being carried out to determine the critical challenges posed by the presence of these plastics in the ecosystem. In this review, the sources of micro- and nanoplastic contamination are described, highlighting their abundance and their environmental fate after being released. Moreover, their role in affecting aquatic organisms and the mechanisms involved are clarified. Some insights into their impacts on human health and the challenges faced by researchers in measuring both types of plastics extracted from biota are also presented. Assessing the toxicological impact of these plastics on sediment and aquatic organisms is an emerging issue, as they have been found in microalgae, brine shrimp larvae, bivalves, fish and shellfish. The amount of plastic waste in the seas is continuing to increase and part of that waste is degraded to produce microplastics and nanoplastics. Therefore, exposure to these materials will inevitably increase, resulting in an emerging food safety issue. Micro- and nanoplastics contamination might cause damage to metabolic, morphological, physiological, food uptake, and behavioral processes, and as a consequence, their impacts may be significant at both the cellular and ecosystem levels. Research output concerning the source, fate, and toxicological impact of micro- and nanoplastics on marine organisms has increased dramatically, but there are still gaps in knowledge about the molecular alterations that they cause.