Maternal effects can dramatically influence the evolutionary process, in some cases facilitating and in others hindering adaptive evolution. Maternal effects have been incorporated into quantitative genetic models using two theoretical frameworks: the variance-components approach, which partitions variance into direct and maternal components, and the trait-based approach, which assumes that maternal effects are mediated by specific maternal traits. Here, we demonstrate parallels between these models and test their ability to predict evolutionary change. First, we show that the two approaches predict equivalent responses to selection in the absence of maternal effects mediated by traits that are themselves maternally influenced. We also introduce a correction factor that may be applied when such cascading maternal effects are present. Second, we use several maternal effect models, as well as the standard breeder's equation, to predict evolution in response to artificial selection on flowering time in American bellflower, Campanulastrum americanum. Models that included maternal effects made much more accurate predictions of selection response than the breeder's equation. Maternal effect models differed somewhat in their fit, with a version of the trait-based model providing the best fit. We recommend fitting such trait-based models when possible and appropriate to make the most accurate evolutionary predictions.