In pigs and broiler chickens, the gastrointestinal tract or gut is subjected to many challenges which alter performance, animal health, welfare and livability. Preventive strategies are needed to mitigate the impacts of these challenges on gut health while reducing the need to use antimicrobials. In the first part of the review, we propose a common definition of gut health for pig and chickens relying on four pillars, which correspond to the main functions of the digestive tract: (i) epithelial barrier and digestion, (ii) immune fitness, (iii) microbiota balance and (iv) oxidative stress homeostasis. For each pillar, we describe the most commonly associated indicators. In the second part of the review, we present the potential of functional amino acid supplementation to preserve and improve gut health in piglets and chickens. We highlight that amino acid supplementation strategies, based on their roles as precursors of energy and functional molecules, as signaling molecules and as microbiota modulators can positively contribute to gut health by supporting or restoring its four intertwined pillars. Additional work is still needed in order to determine the effective dose of supplementation and mode of administration that ensure the full benefits of amino acids. For this purpose, synergy between amino acids, effects of amino acid-derived metabolites and differences in the metabolic fate between free and protein-bound amino acids are research topics that need to be furtherly investigated.