In recent decades, given the important role of gamma-aminobutyric acid (GABA) in human health, scientists have paid great attention to the enrichment of this chemical compound in food using various methods, including microbial fermentation. Moreover, GABA or GABA-rich products have been successfully commercialized as food additives or functional dietary supplements. Several microorganisms can produce GABA, including bacteria, fungi, and yeasts. Among GABA-producing microorganisms, lactic acid bacteria (LAB) are commonly used in the production of many fermented foods. Lactiplantibacillus plantarum (formerly Lactobacillus plantarum) is a LAB species that has a long history of natural occurrence and safe use in a wide variety of fermented foods and beverages. Within this species, some strains possess not only good pro-technological properties but also the ability to produce various bioactive compounds, including GABA. The present review aims, after a preliminary excursus on the function and biosynthesis of GABA, to provide an overview of the current uses of microorganisms and, in particular, of L. plantarum in the production of GABA, with a detailed focus on fermented foods. The results of the studies reported in this review highlight that the selection of new probiotic strains of L. plantarum with the ability to synthesize GABA may offer concrete opportunities for the design of new functional foods.