We look at two aspects of the evolution of RNA. First we look at RNA replication dynamics in an early RNA world context. Experimental evidence (Spiegelman et al. 1965, Biebricher et al. 1981) shows that under some conditions RNA evolves towards small quickly replicating molecules. We investigate what conditions are sufficient for a population of RNA molecules to evolve towards a balanced population of molecules. This is a population not completely dominated by a single length of molecule. We consider two models: A linear model in which indel rate is inversely proportional to length and a game theory model in which reproductive efficiency depends on the distribution of molecule lengths within a population (this is linked to catalytic efficiency). Models are investigated using analytic, numerical and simulation methods. The linear model is not sufficient to support a population with balanced length distribution. Simulation methods show that the game theory model may support such a population. We next look at RNA evolution in the context of RNA virus evolution. Using virus samples taken over a thirty year period we investigate the evolution of Respiratory Syncytial Virus (RSV) in New Zealand. RSV most strongly affects infants and the elderly, causing cold like symptoms in mild cases and bronchiolitis or occasionally death in severe cases. New Zealand has a higher incidence of RSV bronchiolitis per head of population than many other developed countries. We compare New Zealand strains of the virus to those isolated overseas to investigate if New Zealand may have significantly different strains. We look at the evolution of the virus within New Zealand looking for evidence of antigenic drift, as well as analysing substitution rates and selection at individual codon sites. No evidence is found to suggest that New Zealand has significantly different strains of RSV from other countries. We conclude the higher rate of severe RSV in New Zealand must be caused by factors other than virus strain. The portion of the virus analysed shows strong evidence of being under positive selective pressure. This and other analyses suggest that RSV may be undergoing antigenic drift.