Methods for treating diseases or disorders of the skin which are characterized by angiogenesis have been developed using curcumin and curcumin analogs. Based on the results obtained with curcumin, it has been determined that other angiogenesis inhibitors can also be used to treat these skin disorders. It has further been discovered that curcumin acts to inhibit angiogenesis in part by inhibition of basic fibroblast growth factor (bFGF), and thereby provides a means for treating other disorders characterized by elevated levels of bFGF, such as bladder cancer, using curcumin and other analogues which also inhibit bFGF. Representative skin disorders to be treated include the malignant diseases angiosarcoma, hemangioendothelioma, basal cell carcinoma, squamous cell carcinoma, malignant melanoma and Karposi's sarcoma, and the non-malignant diseases or conditions including psoriasis, lymphangiogenesis, hemangioma of childhood, Sturge-Weber syndrome, verruca vulgaris, neurofibromatosis, tuberous sclerosis, pyogenic granulomas, recessive dystrophic epidermolysis bullosa, venous ulcers, acne, rosacea, eczema, molluscum contagious, seborrheic keratosis, and actinic keratosis.