We have studied the decomposition and isomerization of furfural in the gas phase using quantum chemical and statistical reaction rate theory techniques. This work uncovers a variety of new reaction channels in furfural pyrolysis that lead to formation of the experimentally observed products, including CO2, which was previously unexplained. In addition to the known mechanism for furan + CO production, furfural is shown to isomerize directly to 2-pyrone, with a barrier height of 69 kcal mol-1, from where it can decompose to vinylketene + CO (highest barrier of 65 kcal mol-1) or to CO2 + 1,3-cyclobutadiene (highest barrier of 66 kcal mol-1). Alternative pathways to vinylketene + CO and 4-pyrone are also described. An RRKM theory/master equation model is developed to describe reactions on the C5O2H4 surface and used to simulate the decomposition kinetics of furfural and 2-pyrone. For both molecules, decomposition at 1400-2100 K is dominated by the formation of furan + CO, which represents around 75% of the total products, compared to around 19% and 6% for vinylketene + CO and total CO2, respectively. The model also predicts significant formation of stabilized 2-pyrone under these conditions. Rate coefficient expressions are reported as a function of both temperature and pressure for the main decomposition and isomerization channels identified in the pyrolysis of furfural and 2-pyrone, to facilitate detailed chemical kinetic modelling of these important oxygenated hydrocarbons.