Biogenic amines (BAs) can be found in a wide range of meat and meat products, where they are important as an index for product stability and quality, but also for their impact on public health. This review analyzes the scientific evidence gathered so far on the presence and role of biogenic amines in meat and meat products, also considering the effect of technological conditions on BAs accumulation or decrease. The data provided can be useful for developing solutions to control BAs formation during the shelf-life, for example by novel starters for dry cured products, as well as by packaging technologies and materials for fresh meats. Further research, whose trends are reviewed in this paper, will fill the knowledge gaps, and allow us to protect such perishable products along the distribution chain and in the home environment.