Tensions in Cosmology: Interpreting Them Through Inhomogeneous Models

We review a subset of the current tensions affecting the standard $\Lambda$CDM cosmological model, emphasizing the role of chronic systematics and significance inflation in shaping their interpretation. As a unifying framework, we consider the spherically symmetric inhomogeneous $\Lambda$LTB model and use it as a set of "glasses" through which to reinterpret the Hubble, dipole, and dark-energy tensions. Large-scale spatial gradients in this model introduce anisotropic expansion and position-dependent observables, allowing local estimates of $H_{0}$ to shift, dipolar signatures to arise, and an apparently evolving dark-energy equation of state to be mimicked without invoking genuinely dynamical dark energy. We discuss how these effects are constrained once the full supernova, CMB, and large-scale-structure data sets are included, and argue that it remains unclear whether any single $\Lambda$LTB configuration can simultaneously account for all major anomalies. More broadly, we highlight that cosmology currently lacks a widely accepted baseline model that is both theoretically well founded and capable of accommodating the Hubble and dark-energy tensions, leaving us without a true concordance framework for forecasting future surveys.