With the latest results from Planck, we have entered a new era of “precision cosmology”. However, some predictions of the canonical cosmological model namely Lambda-Cold-Dark-Matter (LCDM), calibrated on data from the early universe, are being challenged by high-accuracy measurements with probes of the late-universe. In this talk, I will review the status of two “tensions” that have attracted a lot of attention over the last few years. On the one hand, the Hubble Tension is a mismatch between measurements of the Hubble parameter with a variety of late-universe probes (the cepheid-calibrated  distance ladder in particular) and its prediction from the Planck/LCDM model. On the other hand,  a "S8 tension" has emerged between measurements of the large-scale clustering amplitude  measured via galaxy weak-lensing surveys and that predicted by the Planck/LCDM cosmology. After a brief review of the measurements and (some) possible systematic errors that could affect these measurements, 

I will discuss new physics scenarios that have been suggested and what new  “concordance cosmology” may emerge from these tensions.