Biorefineries are facilities in which lignocellulosic biomasses are converted in a wide range of bioproducts facilitating the transition from the use of petrochemical resources to renewable ones. Organic acids are considered very attractive for their utilization in different industrial areas as building blocks or as final bioproducts leading to a considerable market growth. They are metabolites which are naturally produced by microbials. The production of these molecules by filamentous fungi are attracting more attention due to their ability to hydrolyze lignocellulosic biomasses and to contextually produce different organic acids. Contrarily to a lot of other microorganisms, fungi have the ability to ferment pentoses, broadening the substrate utilization. The integrated use of lignocellulosic biomasses as material input and fungi as biocatalyst can contribute to make biorefineries more successful. This review gives an overview about the lignocellulosic biomass structure and hydrolysis, fungal morphology, and how they are connected. Further, it describes some relevant organic acids with regard to their processes, biocatalysts, industrial applications, and market considerations.