There is almost a consensus that complexity has increased in information living systems, giving rise to symbolicity, grammar, syntactic recursiveness, etc. However, the processes behind the complexification of semiosis and its relation to evolution are not well understood. Moreover, evolution of semiotic complexity can mean different things in different domains. Concretely, many open questions can be asked: What is semiotic complexity? How can semiotic complexity growth be measured in natural living systems? What are the main hypotheses about semiotic complexity growth that can actually be tested? Are the principles of natural selection sufficient to explain the evolution of semiotic complexity in biological systems? How do semiotic systems emerge from reactive systems? How do high level processes (e.g., symbol-based communication) emerge from lower-level processes (e.g., indexical)?