Lignocellulosic biomass from agricultural and agro-industrial residues represents one of the most important renewable resources that can be utilized for the biological production of ethanol. The yeast Saccharomyces cerevisiae is widely used for the commercial production of bioethanol from sucrose or starch-derived glucose. While glucose and other hexose sugars like galactose and mannose can be fermented to ethanol by S. cerevisiae, the major pentose sugars D-xylose and L-arabinose remain unutilized. Nevertheless, D-xylulose, the keto isomer of xylose, can be fermented slowly by the yeast and thus, the incorporation of functional routes for the conversion of xylose and arabinose to xylulose or xylulose-5-phosphate in Saccharomyces cerevisiae can help to improve the ethanol productivity and make the fermentation process more cost-effective. Other crucial bottlenecks in pentose fermentation include low activity of the pentose phosphate pathway enzymes and competitive inhibition of xylose and arabinose transport into the cell cytoplasm by glucose and other hexose sugars. Along with a brief introduction of the pretreatment of lignocellulose and detoxification of the hydrolysate, this review provides an updated overview of (a) the key steps involved in the uptake and metabolism of the hexose sugars: glucose, galactose, and mannose, together with the pentose sugars: xylose and arabinose, (b) various factors that play a major role in the efficient fermentation of pentose sugars along with hexose sugars, and (c) the approaches used to overcome the metabolic constraints in the production of bioethanol from lignocellulose-derived sugars by developing recombinant S. cerevisiae strains.