Observations of the cosmic microwave background (CMB) radiation are described with remarkable accuracy by the six-parameter [Formula: see text]CDM cosmology. However, the key ingredients of this model, namely dark matter, dark energy and cosmic inflation are not understood at a fundamental level. It is, therefore, important to investigate tensions between the CMB and other cosmological probes. I will review aspects of tensions with direct measurements of the Hubble constant [Formula: see text], measurements of weak gravitational lensing, and the recent hints of evolving dark energy reported by the Dark Energy Spectroscopic Instrument (DESI) collaboration.This article is part of the discussion meeting issue 'Challenging the standard cosmological model'.