Biogenic amines (BA) are biomolecules of low molecular weight with organic basic functionalities (amine group) that are formed by the microbial decarboxylation of amino acids of fermented food/beverages. Hence BAs are an important indicator in estimating the freshness and quality of meat, seafood, and industrial food products with high protein content. The reaction of BAs with nitrites available in certain meat products forms nitrosoamine, a carcinogenic compound. Hence BAs are in general considered to be a food hazard and monitoring the level of BAs in food samples becomes crucial as their high concentrations may lead to health problems. This review offers an overview of the available chemical and electrochemical methods that are typically used for the sensing of BAs in food samples. Certain compounds are known to selectively interact with BAs via chemical or non-covalent interactions and these interactions are often accompanied by fluorescence or visible color changes (sometimes visual detection) that could be monitored/assessed using a fluorescence spectrophotometer or UV-vis spectrophotometer (colorimetric methods). The colorimetric methods are limited by sensitivity and selectivity as they are based on straight-forward chemical reactions. In the case of electrochemical sensing of BAs, mediators are often used which undergo oxidation/reduction to produce intermediates that could interact with BAs accompanied by changes in their electrochemical potential. Overall, this review summarizes the available chemical and electrochemical strategies towards the sensing of BAs with a discussion on further prospects.