The presently claimed and disclosed inventive concept(s) provides methods for reducing, reversing or inhibiting retinal cell degeneration, or neovascularization in tissues of a mammalian subject having a pathological condition involving neovascularization, by administration in vivo of nanoceria particles (cerium oxide nanoparticles) to the subject. The method of the presently claimed and disclosed inventive concept(s) is useful, for example, for reducing, treating, reversing or inhibiting degeneration of retinal cells such as photoreceptor cells or neovascularization in ocular tissue such as the retina, macula or cornea; or other tissues such as, but not limited to, skin, synovial tissue, intestinal tissue, or bone. In addition, the method of the presently claimed and disclosed inventive concept(s) is useful for reducing or inhibiting neovascularization in a neoplasm (tumors), which can be benign or malignant and, where malignant, can be a metastatic neoplasm. As such, the presently claimed and disclosed inventive concept(s) is directed to using compositions containing nanoceria particles to reduce, treat, reverse or inhibit angiogenesis in a mammalian subject.