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Dominant shapes naturally emerge in atomic nuclei from first principles, thereby establishing the shape-preserving symplectic Sp(3,\mathbb{R} $ℝ$) symmetry as remarkably ubiquitous and almost perfect symmetry in nuclei. We discuss the critical role of this emergent symmetry in enabling machine-learning descriptions of heavy nuclei, ab initio modeling of\alpha $\alpha$clustering and collectivity, as well as tests of beyond-the-standard-model physics. In addition, the Sp(3,\mathbb{R} $ℝ$) and SU(3) symmetries provide relevant degrees of freedom that underpin the ab initio symmetry-adapted no-core shell model with the remarkable capability of reaching nuclei and reaction fragments beyond the lightest and close-to-spherical species. 

We review the ab initio symmetry-adapted (SA) framework for determining the structure of stable and unstable nuclei, along with related electroweak, decay, and reaction processes. This framework utilizes the dominant symmetry of nuclear dynamics, the shape-related symplectic [Formula: see text] symmetry, which has been shown to emerge from first principles and to expose dominant degrees of freedom that are collective in nature, even in the lightest species or seemingly spherical states. This feature is illustrated for a broad scope of nuclei ranging from helium to titanium isotopes, enabled by recent developments of the ab initio SA no-core shell model expanded to the continuum through the use of the SA basis and that of the resonating group method. The review focuses on energies, electromagnetic transitions, quadrupole and magnetic moments, radii, form factors, and response function moments for ground-state rotational bands and giant resonances. The method also determines the structure of reaction fragments that is used to calculate decay widths and α-capture reactions for simulated X-ray burst abundance patterns, as well as nucleon–nucleus interactions for cross sections and other reaction observables.