LCDM is the most successful cosmology model in the past decades, proven by multiple independent observations including CMB, Supernovae, Large scale structures, etc. LCDM states that our flat universe (mostly) consists of dark matter and dark energy. However, as the precision of cosmological probes increases, some anomalies that cannot be perfectly explained by LCDM start to show up. Among them the most statistically significant one is the 4-5 \sigma discrepancy between early and late universe Hubble constant. In this talk, I will briefly summarize the facts we know about Hubble constant measurements, and present the current discussions in the field on the Hubble tension. After that, I will use my recent effort on resolving this tenison by decaying dark matter cosmology as an example, to demonstrate where such anomalies lead us to and how we explore beyond LCDM.