The many tensions with dark-matter based models and implications on the nature of the Universe

(Abridged) Fundamental tensions between observations and dark-matter based cosmological models have emerged. This updated review has two purposes: to explore new tensions that have arisen in recent years, compounding the unresolved tensions from previous studies, and to use the shortcomings of the current theory to guide the development of a successful model. Tensions arise in view of the profusion of thin disk galaxies, the pronounced symmetrical structure of the Local Group of Galaxies, the common occurrence of planes of satellite systems, the El Gordo and Bullet galaxy clusters, significant matter inhomogeneities on scales much larger than 100 Mpc, and the observed rapid formation of galaxies and super-massive black holes at redshifts larger than 7. Given the nature of the tensions, the real Universe needs to be described by a model in which gravitation is effectively stronger than Einsteinian/Newtonian gravitation at accelerations below Milgrom's acceleration scale. The promising nuHDM model, anchored on Milgromian dynamics but keeping the standard expansion history with dark energy, solves many of the above tensions. However galaxy formation appears to occur too late in this model, model galaxy clusters reach too large masses, and the mass function of model galaxy clusters is too flat and thus top-heavy in comparison to the observed mass function. Classes of models that reassess inflation, dark energy and the role of the CMB should be explored.