The central aim of this Special Issue, devoted to a multifocal study of the geometry and phenomenology of the living, is to show the need of working with models that integrate geometrical and topological objects and operations, dynamical variables and specific biological mechanisms and their relationships with one another. A multilevel and integrative approach has essentially to consider the fact that simply knowing the parts list of genes and proteins does not tell us much about how life’s many biological processes works. The cellular organization is a complex dynamical system with hundreds of thousands of bio-molecules interacting with one another to execute organism’s many related functions. It is argued that the production of complex living organisms owes much of its working to some topological mechanisms (i.e. four-dimensional transformations and deformations) which operate markedly on the three levels of the organization, regulation and evolution of biological systems. Thus, one can speak of a specific topology of the living acting very dynamically on the (non-fixed) substrate space of the physiological and metabolic activities of all complex living organisms. Philosophically, it is now clear that the genetic causality theory has several limitations, both intrinsic because of the multilevel complexity of biological processes, and extrinsic in that it disregards the influence of the phenotype on the genotype and in particular the possibility that certain acquired characteristics can be inherited. In a sense, we can say that the molecular biological conception of recent decades has limited or even misleadingly impacted our vision of the living world. New ideas are needed if we are to succeed in unravelling multifactorial genetic, epigenetic and environmental causation at higher levels of physiological function and so to explain fundamental living phenomena that genetics alone is unable to explain. Some of the most significant conclusions proposed in this issue are that (i) structural plasticity and biological functionality are deeply related, (ii) the biological information and signification is inherently spatial and temporal, it is not unidirectional, and it essentially evolve following a complex and changing network-like organization, (iii) finally, gene ontology is incomplete and it as to be supplied by integrating other fundamental levels of the organization and regulation of the living systems.