In biology, phenotypes' variability stems from stochastic gene expression as well as from intrinsic and extrinsic fluctuations that are largely based on the contingency of evolutionary and developmental paths and on ecosystemic changes. Both forms of randomness constructively contribute to biological robustness, as resilience, far away from conventional computable dynamics, where elaboration and transmission of information are robust when they resist to noise. We first survey how fluctuations may be inserted in biochemical equations as probabilistic terms, in conjunction to diffusion or path in-tegrals, and treated by statistical approaches to physics. Further work allows to better grasp the role of biological " resonance " (interactions between different levels of organization) and plasticity, in a highly unconventional frame that seems more suitable for biological processes. In contrast to physical conservation properties, thus symmetries, symmetry breaking is particularly relevant in biology; it provides another key component of biological historicity and of randomness as a source of diversity and, thus, of onto-phylogenetic stability and organization as these are also based on variation and adaptativity.