The growth and operation of all living beings are directed by the interpretation, in each of their cells, of a chemical program, the DNA string or genome. This process is the source of inspiration for the Embryonics (embryonic electronics) project, whose final objective is the design of highly robust integrated circuits, endowed with properties usually associated with the living world: self-repair (cicatrization) and self-replication. The Embryonics architecture is based on four hierarchical levels of organization: 1) the basic primitive of our system is the molecule, a multiplexer-based element of a novel programmable circuit; 2) a finite set of molecules makes up a cell, essentially a small processor with an associated memory; 3) a finite set of cells makes up an organism, an application-specific multiprocessor system; 4) the organism can itself replicate, giving rise to a population of identical organisms. In this paper, we provide an overview of our latest research in the domain of the self-replication of processing elements within a programmable logic substrate, a key prerequisite for achieving system-level fault tolerance in our bio-inspired approach.