  The Cosmological Principle (CP) -- the notion that the Universe is spatially
isotropic and homogeneous on large scales -- underlies a century of progress in
cosmology. It is conventionally formulated through the
Friedmann-Lema\^itre-Robertson-Walker (FLRW) cosmologies as the spacetime
metric, and culminates in the successful and highly predictive
$\Lambda$-Cold-Dark-Matter ($\Lambda$CDM) model. Yet, tensions have emerged
within the $\Lambda$CDM model, most notably a statistically significant
discrepancy in the value of the Hubble constant, $H_0$. Since the notion of
cosmic expansion determined by a single parameter is intimately tied to the CP,
implications of the $H_0$ tension may extend beyond $\Lambda$CDM to the CP
itself. This review surveys current observational hints for deviations from the
expectations of the CP, highlighting synergies and disagreements that warrant
further study. Setting aside the debate about individual large structures,
potential deviations from the CP include variations of cosmological parameters
on the sky, discrepancies in the cosmic dipoles, and mysterious alignments in
quasar polarizations and galaxy spins. While it is possible that a host of
observational systematics are impacting results, it is equally plausible that
precision cosmology may have outgrown the FLRW paradigm, an extremely pragmatic
but non-fundamental symmetry assumption.
