Furan-based polymers are renewable alternatives for traditional fossil-based polymers, therefore carrying enormous potential for improved sustainability. Many aspects of these novel polymers still need to be investigated more comprehensively for full appreciation of their applicability. Here, the degradation of furan-based polymers including poly(butylene furanoate), poly(butylene bifuranoate), and three random copolyesters thereof were investigated under artificial weathering conditions for up to 300 h. This included simultaneous exposure of film samples to ultraviolet light, high humidity, and elevated temperature. Poly(ethylene terephthalate) was used as a reference material. Both the pristine and weathered samples were characterized using infrared spectroscopy, differential scanning calorimetry, and dynamic mechanical analysis, among others. According to the infrared measurements, the exposed surfaces of the films had undergone severe chemical changes. Indications of covalent cross-linking after exposure to ultraviolet light were found in differential scanning calorimetry, dynamic mechanical analysis, and dissolution experiments. The nature of the cross-linking mechanisms and exact structure of the formed degradation products remain unclear. It is concluded that polyesters derived from both 2,5-furandicarboxylic and 2,2 '-bifuran-5,5 '-dicarboxylic acids are relatively labile when exposed to UV light. The latter monomer appears especially labile, probably in part because of its broader and elevated UV absorbance. Simple oven-aging in air indicated that crosslinking also occurred in the absence of UV, but the overall chemical degradation was stronger in the weathering conditions. In the more easily crystallizable samples, the aging-induced crystallization played an important role in the final physical properties.