Among vertebrates, passerine birds are an exceptionally diverse group (>6,000 living species) encompassing more than half of living bird diversity. In this thesis I present primary descriptive anatomical work (Chapters 2 & 4), phylogenetic inference (Chapter 2), and novel quantitative approaches (Chapters 3 & 4) to shed light on aspects of passerine evolutionary history and diversification. Chapter 2 comprises a novel, comprehensive anatomical dataset of the passerine carpometacarpus, an anatomically variable bone in the wing. Using these data, I attempt to elucidate the phylogenetic affinities of several early passerine fossils from the Oligocene of Europe using Bayesian phylogenetic analyses of discrete carpometacarpus characters with a large-scale taxon sample encompassing >70% of passerine family-level clades. My results provide evidence that crown group suboscines (one of the two primary clades of passerine birds) were present in Europe by the early Oligocene, and that crown group oscines (the other primary clade of passerines) were present by the late Oligocene. Inadvertently, this project revealed evidence of pervasive convergent evolution, or homoplasy, in the passerine carpometacarpus. In Chapter 3, I present a new method of quantifying homoplasy in discrete character datasets and re-evaluate longstanding hypotheses about expected patterns of homoplasy considering changing variables in phylogenetic datasets. Through analyses of simulated and empirical datasets, I show that my new metric, the ‘relative homoplasy index’, outperforms the two most frequently used methods in the literature—the retention index and consistency index—in terms of accurately measuring homoplasy in discrete matrices. I also show that, contrary to expectations based on previous studies, relative homoplasy within phylogenetic matrices decreases as taxa are added to phylogenetic datasets. These results indicate that passerines exhibit high levels of homoplasy compared to other bird datasets. In Chapter 4, I investigate evolutionary constraints in the passerine wing and hindlimb skeleton. With my carpometacarpus dataset from Chapter 2 and an additional novel discrete anatomical dataset for the passerine tarsometatarsus (foot), I explore patterns of homoplasy and character state exhaustion across the two major sister clades of passerines, Tyranni (suboscines) and Passeri (oscines). I show that oscines, the more diverse subclade in terms of present-day species richness, exhibits substantially more homoplasy in the appendicular skeleton than suboscines. Simulated null distributions of character state exhaustion patterns reveal that oscines evolved under significant constraints to morphological diversification, whereas suboscines did not. Within discrete character morphospace for the carpometacarpus and tarsometatarsus, oscines show highly overlapping subclades, in contrast to pronounced separation among suboscine subclades; these results indicate differences in the mode of evolution for oscines and suboscines, which have culminated in greater levels of convergence among oscines. This thesis lays the foundation for future work investigating passerine macroevolution and constitutes an important step in broadening our understanding of how passerines became so spectacularly diverse.