Especially due to the unconscious use of petroleum products, the ocean faces a potential danger: $\textit{plastic pollution}$. Plastic pollutes not only the ocean but also directly the air and foods whilst endangering the ocean wild-life due to the ingestion and entanglements. Especially, during the last decade, public initiatives and academic institutions have spent an enormous time on finding possible solutions to marine plastic pollution. Remote sensing imagery sits in a crucial place for these efforts since it provides highly informative earth observation products. Despite this, detection, and monitoring of the marine environment in the context of plastic pollution is still in its early stages and the current technology offers possible important development for the computational efforts. This paper contributes to the literature with a thorough and rich review and aims to highlight notable literature milestones in marine debris monitoring applications by promoting the computational imaging methodology behind these approaches.