Agricultural residues pose a valuable resource. Through microbial fermentations, a variety of products can be obtained, ranging from fuels to platform chemicals. Depending on the nature of the organic residue, pretreatment and hydrolysis are needed prior to fermentation in order to release fermentable sugars. Continuous set-ups are common for the production of methane or ethanol from lignocellulosic biomass, however, this does not apply for the fermentative generation of biochemicals, an approach that conserves chemical functionality present in biomass. Certainly, continuous set-ups could beneficially contribute to bioeconomy by providing techniques allowing the production of biochemicals in a sustainable and efficient way. This review summarizes research conducted on the continuous pretreatment, hydrolysis, and fermentation of lignocellulosic biomass, and particularly towards the production of the biobased molecules: Succinic and lactic acid.