The concordance or standard Λ Cold Dark Matter (ΛCDM) model is a well-defined, predictive and simple cosmological model. A number of challenges of the standard ΛCDM model have been emerging during the past few years, which has been summarized by recent reviews.
In this talk, I will give a brief introduction to several existing signals in cosmological and astrophysical data that appear to be in some tension. I focus on three parts: H0 tension, large-scale anomalies (extreme spatial distribution of the radio galaxies) and small-scale curiosities (the core-cusp, missing satellite, too big to fail, the plane of satellites). Because this topic is so large, I just generally discuss what it is and the possible explanations.
