The strongly interacting system created in ultrarelativistic nuclear collisions behaves almost as an ideal fluid with rich patterns of the velocity field exhibiting strong vortical structure. Vorticity of the fluid, via spin-orbit coupling, leads to particle spin polarization. Due to the finite orbital momentum of the system, the polarization on average is not zero; it depends on the particle momenta reflecting the spatial variation of the local vorticity. In the last few years, this field experienced a rapid growth due to experimental discoveries of the global and local polarizations. Recent measurements triggered further development of the theoretical description of the spin dynamics and suggestions of several new mechanisms for particle polarization. In this review, we focus mostly on the experimental results. We compare the measurements with the existing theoretical calculations but try to keep the discussion of possible underlying physics at the qualitative level. Future measurements and how they can help to answer open theoretical questions are also discussed. We pay a special attention to the employed experimental methods, as well as to the detector effects and associated corrections to the measurements.

We review model calculations of exclusive vector meson production in ultraperipheral heavy ion collisions. We highlight differences and similarities between different dipole models and leading twist shadowing calculations. Recent color glass condensate calculations are presented with focus on effects from nuclear structure and azimuthal anisotropies driven by interference effects.

Numerous phenomenological nuclear models have been proposed to describe specific observables within different regions of the nuclear chart. However, developing a unified model that describes the complex behavior of all nuclei remains an open challenge. Here, we explore whether novel symbolic Machine Learning (ML) can rediscover traditional nuclear physics models or identify alternatives with improved simplicity, fidelity, and predictive power. To address this challenge, we developed a Multi-objective Iterated Symbolic Regression approach that handles symbolic regressions over multiple target observables, accounts for experimental uncertainties and is robust against high-dimensional problems. As a proof of principle, we applied this method to describe the nuclear binding energies and charge radii of light and medium mass nuclei. Our approach identified simple analytical relationships based on the number of protons and neutrons, providing interpretable models with precision comparable to state-of-the-art nuclear models. Additionally, we integrated this ML-discovered model with an existing complementary model to estimate the limits of nuclear stability. These results highlight the potential of symbolic ML to develop accurate nuclear models and guide our description of complex many-body problems.