This article provides a comprehensive and critical review of the latest studies on catalytic glycerol dehydration-oxidation to acrylic acid. The two-bed catalytic system in one or two reactors involves glycerol dehydration to acrolein and subsequent oxidation of acrolein to acrylic acid. Zeolites, metal oxides, heteropoly acids, and phosphates are effective in the dehydration of glycerol to acrolein. Mo-V-O catalysts appear active in the acrolein oxidation to acrylic acid. The glycerol can be completely converted to acrolein with 98% selectivity. In such a two-step process, the step of catalytic dehydration is thought to be critical. A few recent studies reveal that the conversion of glycerol to acrylic acid in two reactors can be also achieved via allyl alcohol as intermediate. For the one-bed catalytic glycerol oxydehydration to acrylic acid, a single catalyst must possess both active acid sites and active redox sites. Mo-V-O, W-V-O, Mo-V-W-O, W-V-Nb-O oxide catalysts, and heteropoly acid catalysts are particularly promising. Currently, a 60% yield of acrylic acid can be achieved over H0.1Cs2.5(VO)(0.2)(PMo12O40)(0.25)(PW12O40)(0.75) at 340 degrees C. However, all the catalysts rapidly deactivate due to coking. Coking usually occurs during the glycerol oxydehydration step. Optimizing reaction conditions such as increasing water and oxygen feeding, lowering reaction temperature, tuning the catalysts by finely doping, adjusting the surface acidity and enlarging pores of the solid catalysts can inhibit coking to some extent by slowing the deactivation of catalyst. Yet coking over catalysts is a major obstacle when conducting glycerol oxydehydration on a large scale. We suggest that future work should place an emphasis on revealing the essence of coking, further designing coking-resisting catalysts, and developing an efficient reaction and separation system.