The origin of life has always attracted scientific inquiries. The RNA world hypothesis, which is currently considered to be the most plausible scenario for the origin of life, posits that, before the evolution of DNA and proteins, primordial life was based on RNA for both genetic information storage and chemical catalysis. In its simplest form, the RNA world consists of RNA molecules that can replicate themselves. How can a system of such simple replicators evolve into life as we know it? To put it differently, how can a system of simple RNA-like replicators increase its complexity through Darwinian evolution? This thesis approaches this question from a view point of bioinformatics (the studies of informational processes in biotic systems). Mathematical or computational models are used to obtain novel insights into the evolutionary dynamics of RNA-like replicator systems. The thesis begins with a review of the past studies including those of the author''s and then presents each of the author''s studies in detail. The thesis should be of interest to researchers and students who are interested in the origin of life, prebiotic evolution, evolutionary biology and theoretical biology.