The current standard models of cosmology (SMoC) -
specifically LCDM and warm dark matter models - served for
a few decades as the basis of research in astronomy and cosmology,
and have been studied extensively. However, fundamental tensions
between observations and theory 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.

In any representative volume, more than 90 per cent of all galaxies
have thin, extended star-forming ancient disks. But these
structures are too fragile to withstand the repeated mergers that
dark matter would induce. According to SMoC cosmological
simulations, galaxies in the Local Group around the Mpc scale should
be distributed in a spheroidal configuration. Observations show that
they are instead arranged in thin planes. This poses major questions
on the nature and dynamical history of the Local Group.
Furthermore, there exist mutually correlated planes of satellite
dwarf galaxies located around the Andromeda and Milky Way
galaxies. These planes may have been created by the tidal forces
generated by a previous encounter between the two galaxies. Also the
configuration of the nearby M81 group poses challenges to the
SMoC. None of these structures could exist in the presence of dark
matter, because dynamical dissipation would cause the galaxies to
merge within a Gyr time scale. In addition, the El Gordo galaxy
cluster has been observed at a redshift at emission of
z=0.87 to already have reached a mass of
about 2 x 10^{15} Msun, being impossible in the SMoC.
In the light of the growing evidence for large-(>few
hundred Mpc)-scale inhomogeneities, we have shown that the Hubble
Tension is simply caused by the matter bulk flows of the large scale
structure. These observations suggest that the Universe is more
inhomogeneous and that structures grow more rapidly than what is
allowed by the SMoC on the Gpc~scale. Novel tensions have emerged
from observations of the early Universe. For instance, galaxies of
mass 10^9-10^{10} Msun have been detected in the redshift
range of 10 < z < 20, indicating a faster
galaxy formation than predicted in the SMoC. An independent
indication for such early galaxy formation comes from the downsizing
timescales of early-type galaxies and their associated rapid
formation of central super-massive black holes (SMBHs).

We discuss a few candidate models of cosmology from the literature,
but most fail on all or a number of the above problems. 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. Interestingly, Milgromian dynamics (MOND)
coincides with the generalized Poisson equation given by the
non-linear p-Laplacian when p=3 with p=2 providing the standard
Newtonian Poisson equation. A promising model that solves several of
the above tensions is nuHDM. While it embraces MOND, eliminating
the need for dark matter, it retains dark energy and consequently
the SMoC expansion history. 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.

The above mentioned evidence casts doubts on the viability of dark
matter and dark energy as fundamental components of the Universe,
with severe consequences. Specifically, the Hot Big Bang Theory
cannot provide a good fit to the CMB power spectrum without invoking
both of these components. Consequently, inflation - introduced to
justify why causally-disconnected regions of the CMB should be
homogeneous on a flat geometry - would also cease to be needed. The
models that have been simulated to-date with these boundary
conditions appear to not be able to generate structure rapidly
enough to be consistent with the high-redshift JWST observations.
Given all the noted anomalies, the classes of models that relax
these boundary conditions should be explored.