Common toxic compounds 2-furaldehyde (furfural) and 5-hydroxymethyl-2-furaldehyde (HMF) are formed from dehydration of pentose and hexose, respectively, during decomposition of lignocellulosic biomass polymers. Furfural and HMF represent a major class of aldehyde toxic chemicals that inhibit microbial growth and interfere with subsequent fermentation for production of renewable fuels and chemicals. Understanding mechanisms of yeast tolerance aids development of tolerant strains as the most economic means to overcome the toxicity. This review updates current knowledge on yeast resistance to these toxic chemicals obtained from rapid advances in the past few years. Findings are largely exemplified by an adapted strain NRRL Y-50049 compared with its progenitor, the industrial yeast Saccharomyces cerevisiae type strain NRRL Y-12632. Newly characterized molecular phenotypes distinguished acquired resistant components of Y-50049 from innate stress response of its progenitor Y-12632. These findings also raised important questions on how to address more deeply ingrained changes in addition to local renovations for yeast adaptation. An early review on understandings of yeast tolerance to these inhibitory compounds is available and its contents omitted here to avoid redundancy. Controversial and confusing issues on identification of yeast resistance to furfural and HMF are further clarified aiming improved future research. Propositions and perspectives on research understanding molecular mechanisms of yeast resistance and future improvements are also presented.