The paper discusses the challenges and progress in addressing the tensions within theΛCDM (Lambda Cold Dark Matter) cosmological model. It emphasizes the importance of conducting consistency checks of theΛCDM model at different redshifts or scales to localize missing physics. The authors review the hierarchy of assumptions underlyingΛCDM, including General Relativity, the cosmological principle, and the Friedmann-Lemaître-Robertson-Walker (FLRW) metric. They highlight the need to relax these assumptions to resolve tensions in the Hubble constant ($H_0$) and the amplitude of matter fluctuations ($S_8$). The paper argues that the most effective way to localize missing physics is through redshift-dependent fitting parameters ofΛCDM, rather than delocalizing the problem to higher redshifts or scales. Recent progress in understanding the $S_8$ tension and the implications for $H_0$ tension are discussed, suggesting that both tensions point to problems with the backgroundΛCDM cosmology. The authors conclude by emphasizing the importance of conducting consistency checks to either confirm model breakdown or identify unexplored systematics.The paper discusses the challenges and progress in addressing the tensions within theΛCDM (Lambda Cold Dark Matter) cosmological model. It emphasizes the importance of conducting consistency checks of theΛCDM model at different redshifts or scales to localize missing physics. The authors review the hierarchy of assumptions underlyingΛCDM, including General Relativity, the cosmological principle, and the Friedmann-Lemaître-Robertson-Walker (FLRW) metric. They highlight the need to relax these assumptions to resolve tensions in the Hubble constant ($H_0$) and the amplitude of matter fluctuations ($S_8$). The paper argues that the most effective way to localize missing physics is through redshift-dependent fitting parameters ofΛCDM, rather than delocalizing the problem to higher redshifts or scales. Recent progress in understanding the $S_8$ tension and the implications for $H_0$ tension are discussed, suggesting that both tensions point to problems with the backgroundΛCDM cosmology. The authors conclude by emphasizing the importance of conducting consistency checks to either confirm model breakdown or identify unexplored systematics.