For all viruses, replicative success is a balancing act. As obligate intracellular parasites, viruses must overcome or evade a gauntlet of host barriers and defenses while simultaneously maintaining many other required interactions. In instances of cross-species transmission, this balance is often disrupted as a foreign virus encounters a new suite of host-specific selective challenges and must reach a new equilibrium within the context of the biology and ecology of the recipient host species. Thus, the ultimate outcome of viral cross-species transmissions is determined by differential selective pressures and evolutionary changes. Understanding the evolutionary mechanisms that underlie viral transmission to and sustained circulation in a new host species is therefore critical for efforts towards managing ongoing viral epidemics and minimizing the threat of future emergence events. While much of scientific literature in this area focuses on viruses that have already caused significant epidemics or pandemics in humans, viral host-range shifts also occur in other animals. These events can provide tractable and informative models that reveal the critical underlying processes. In addition to their relevancy as companion animals, dogs serve as particularly useful host model systems for studying the drivers of viral emergence as they display many biological and ecological factors that are relevant to emerging infectious diseases in humans. Over the last half century, three viruses from two different families have emerged in dogs as a result of cross-species transmission events: two distinct canine influenza virus (CIV) subtypes – H3N8 and H3N2, and canine parvovirus (CPV). Using these viruses as case studies, this thesis explores the critical steps that occur in viral host-range shifts across multiple biological scales by utilizing new advances in viral full-genome sequencing and preforming sequence analyses informed by detailed epidemiological modeling and viral protein structural information. Among the CIVs, I find that contact heterogeneity within the United States dog population is likely a major barrier preventing sustained circulation. This barrier has proven to be insurmountable for the H3N8 CIV, which has now gone extinct. The circulation of H3N2 CIV appears to be similarly affected; however, my work reveals that multiple re-introductions of virus from Asia have driven repeated epidemic waves within the United States, suggesting that dog populations in Asia serve as a reservoir for this virus. In contrast, CPV is not as limited by host contact heterogeneity, likely due to its broad host range and ability to remain infectious for long periods of time in the environment, both features which increase the probability of exposure to new susceptible animals. However, there appear to be genetic constraints on the small ssDNA CPV genome since after 40 years of sustained pandemic circulation in dogs, I found very low levels of diversity at the intrahost and epidemiological scales. Interestingly, these genetic constraints may be overcome by structural flexibility in the CPV capsid and its interactions with the transferrin receptors from different host species, suggesting an alternative evolutionary strategy for overcoming host-specific barriers to infection. The results of this dissertation provide new information that is immediately relevant to significant ongoing epidemics of viral diseases in dogs and may inform vaccine development and biosecurity or outbreak management practices. In a more general sense, the results also provide a framework for better understanding the critical barriers associated with viral host-range shifts and how different viruses may overcome such barriers.