One of the primary objectives of infectious disease research is uncovering the direct link that exists between viral population dynamics and molecular evolution. For RNA viruses in particular, evolution occurs at such a rapid pace that epidemiological processes become ingrained into gene sequences. Conceptually, this link is easy to make: as RNA viruses spread throughout a population, they evolve with each new host infection. However, developing a quantitative understanding of this connection is difficult. Thus, the emerging discipline of phylodynamics is centered on reconciling epidemiology and phylogenetics using genetic analysis. Here, we present two research studies that draw on phylodynamic principles in order to characterize the progression and evolution of the Ebola virus and the human immunodefficiency virus (HIV). In the first study, the interplay between selection and epistasis in the Ebola virus genome is elucidated through the ancestral reconstruction of a critical region in the Ebola virus glycoprotein. Hence, we provide a novel mechanistic account of the structural changes that led up to the 2014 Ebola virus outbreak. The second study applies an approximate Bayesian computation (ABC) approach to the inference of epidemiological parameters. First, we demonstrate the accuracy of this approach with simulated data. Then, we infer the dynamics of the Swiss HIV-1 epidemic, illustrating the applicability of this statistical method to the public health sector. Altogether, this thesis unravels some of the complex dynamics that shape epidemic progression, and provides potential avenues for facilitating viral surveillance efforts.