Seafood products are highly perishable, owing to their high water activity, close to neutral pH, and high content of unsaturated lipids and non-protein nitrogenous compounds. Thus, such products require immediate processing and/or packaging to retain their safety and quality. At the same time, consumers prefer fresh, minimally processed seafood products that maintain their initial quality properties. The present article aims to review the literature over the past decade on: (i) innovative, individual packaging technologies applied to extend the shelf life of fish and fishery products, (ii) the most common combinations of the above technologies applied as multiple hurdles to maximize the shelf life of seafood products, and (iii) the respective food packaging legislation. Packaging technologies covered include: Modified atmosphere packaging; vacuum packaging; vacuum skin packaging; active food packaging, including oxygen scavengers; carbon dioxide emitters; moisture regulators; antioxidant and antimicrobial packaging; intelligent packaging, including freshness indicators; time–temperature indicators and leakage indicators; retort pouch processing and edible films; coatings/biodegradable packaging, used individually or in combination for maximum preservation potential.