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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 experimental system where the replicators are constantly broken down into building blocks, and where the latter replicate again. Computer simulations allow the determination of optimal energy coupling conditions for such systems. In Chapter 4, information exchange pathways in peptide fibres were studied. The results show that the exchange of building blocks from one fibre to another one takes place at the extremities thereof, while building blocks in the fibre cores are hardly used in the replication of other fibres. These are therefore protected from replication and the information that they carry can hardly be exchanged, unless the fibres continuously break into smaller pieces. While in our experiments Darwinian evolution does not yet take place, we could observe significant processes for enabling Darwinian evolution: exponential growth of fibres, destruction of replicators and selective exchange of building blocks.