Several organic acids have been indicated among the top value chemicals from biomass. Lignocellulose is among the most attractive feedstocks for biorefining processes owing to its high abundance and low cost. However, its highly complex nature and recalcitrance to biodegradation hinder development of cost-competitive fermentation processes. Here, current progress in development of single-pot fermentation (i.e., consolidated bioprocessing, CBP) of lignocellulosic biomass to high value organic acids will be examined, based on the potential of this approach to dramatically reduce process costs. Different strategies for CBP development will be considered such as: (i) design of microbial consortia consisting of (hemi)cellulolytic and valuable-compound producing strains; (ii) engineering of microorganisms that combine biomass-degrading and high-value compound-producing properties in a single strain. The present review will mainly focus on production of organic acids with application as building block chemicals (e.g., adipic, cis,cis-muconic, fumaric, itaconic, lactic, malic, and succinic acid) since polymer synthesis constitutes the largest sector in the chemical industry. Current research advances will be illustrated together with challenges and perspectives for future investigations. In addition, attention will be dedicated to development of acid tolerant microorganisms, an essential feature for improving titer and productivity of fermentative production of acids.