Challenges to the Lambda CDM cosmology

Observations of the cosmic microwave background (CMB) anisotropies provide strong evidence in support of the LCDM cosmology. Nevertheless, a number of 'tensions' have emerged. I will review: (a) recent results from the CMB that have strengthened the evidence in favour of lambda CDM; (b) why it is difficult to explain the discrepancy between the lambda CDM value of the Hubble constant, H0, and the value derived from the Cepheid distance scale; (c) why cosmic shear surveys may indicate a small-scale/large-scale mismatch rather than an inconsistency between early and late time physics; (d) why the recent DESI results suggesting evolving dark energy may be driven by systematic errors; (e) why inflation, a cornerstone of the lambda CDM model, has introduced a new hierarchy problem in cosmology.