Self-replicating molecules play a fundamental role in origins of life studies.In Chapter 2, evidence is provided that specific self-replicating molecules are capable of growing exponentially. This is a very important breakthrough: exponentially growing replicators are better prone to survive during Darwinian evolution. Almost all replicators discovered up to the latest years were not capable of exponential growth.Primordial life likely resulted from repeated attempts of replication in a destructive environment. This replication and destruction process is at the core of Darwinian evolution. In Chapter 3, such a replication/destruction system is studied experimentally and computationally. Based on these studies, it is possible to set up an ex...