Soft polymer networks have seen an explosion of recent developments motivated by new high tech applications in the biomedical field or in engineering. We present a candid and critical overview of the current understanding of the relation between the structure and molecular architecture of polymer networks and their mechanical properties, restricting ourselves to soft networks made of flexible polymers and displaying entropic elasticity. We specifically review and compare recent approaches to synthesize swollen hydrogels with enhanced toughness, resilient but tough unfilled elastomers and self-healing networks containing dynamic bonds. The purpose is less to draw a comprehensive catalogue of approaches than to identify and unify the underlying principles controlling toughening mechanisms and mechanical self-healing behavior and to point out remaining challenges.