Biological information processing and maintenance of life mainly utilise dynamical structures at different levels from a nanoscopic up to a macroscopic scale. Providing a high degree of reliability, reproducibility, unambiguousness, and addressability, underlying compositional processes appear as ideal candidates to perform computational tasks in a discretised manner. In this essay, we consider four levels in which dynamical structures enable an efficient handling with information: (1) the molecular level, (2) the level of reaction network modules, (3) the level of membranes, and (4) the level of higher-order organisms and populations. All of them have in common the capability of controlled memory-based state transitions and hence dedicated systems's configurations encoding behavioural patterns. Due to its discrete algebraic nature, membrane systems represent advantageous frameworks in order to formalise corresponding activities. This in turn paves the way towards efficient tools inspired by nature with manifold smart applications in engineering, computer science, and systems biology. We illustrate membrane system's abilities, benefits, and progress for coping with dynamical structures from an integrative perspective.