Brain digital twins aim to provide faithful, individualized computational representations of brains as dynamical systems, enabling mechanistic understanding and supporting prediction of clinical interventions. Yet current approaches remain fragmented across data pipelines, model classes, temporal scales, and computing platforms, which prevents the preservation of execution semantics across the end-toend workflow. This survey introduces physically constrained executability as a unifying perspective for comparing approaches at the level of execution: whether an execution state is persistent, which events are permitted to update it (simulation, measurement, actuation), and how strongly execution is temporally and causally coupled to neurobiological dynamics. Building on modeling and simulation theory, I propose a taxonomy of execution regimes ranging from isolated offline models to coordinated co-simulation, to continuously executing digital twins sustained by online data assimilation, and ultimately to neuro-neuromorphic physical systems in which biological and computational dynamics are co-executed under shared physical constraints. The executability concept clarifies why accuracy alone is insufficient, and motivates an agenda centered on semantic interoperability, hybrid-time correctness, evaluation protocols, scalable reproducible workflows, and safe closed-loop validation. This survey adopts a systems and runtime-oriented perspective, enabling comparison of heterogeneous approaches based on their execution semantics rather than on model form or application domain alone.

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