Described is a system and method by which text elements to be rendered on a computer display (e.g., paragraph, line or any subset of text including a character or glyph) may be individually or collectively animated, at an author-selected level of granularity. Animation of text may be specified by setting animation properties via direct coding (e.g., in markup) or by specifying animation code to execute on text-related data, just prior to rendering. The text to animate may be static, or dynamically obtained at runtime from an external source. The text to animate is maintained as a whole with other text of the same element, in a text object, until a processing level that produces separate glyph runs, with an animation transform associated with each glyph run to be animated. Also described is an API that supports text animation.