One continuous experiment has been run in macroevolution: the evolution of life on the planet. Therefore, a difficulty in studying macroevolution is the inability to perform controlled experiments over million-year timescales. Model-based approaches provide a powerful alternative avenue in answering questions regarding the deep time evolution of the various diversity and disparity of traits observed in both living and fossil taxa. In my dissertation, I develop and apply novel model-based approaches in investigating drivers of trait evolution over macroevolutionary timescales. Chapter 1 examines how North American mammalian predators responded to climate change over the past 65 million years. Using model selection, I show mammalian predators undergo a shift to more carnivorously adapted assemblages following the expansion of grasslands in North America 33.9 million years ago. Chapter 2 studies the drivers and constraints of color diversity in the bird family Thraupidae (tanagers). As color is a non-linear measurement, I develop a wrapped Brownian motion model for circular datasets. Rates of color evolution in tanagers are lowest in the wings compared to those in the head, throat, breast, and other body patches, signaling the potential structural constraint of flight driving how tanagers navigate through color space. Chapter 3 explores the macroevolutionary ratchet as a mechanism of decline using simulations. Clades evolving under a macroevolutionary ratchet will exhibit distinct tree shape. However, after removing fossil taxa, the signature of the macroevolutionary ratchet quickly disappears, prevent accurate detection of such scenarios using only extant taxa. Overall, this dissertation research showcases the flexibility and power of model-based approaches in understand the evolution of various traits. The development of such quantitative methods will allow for additional macroevolutionary questions to be addressed by the broader research community and give further insights into the drivers of trait evolution in deep time.