The TeV extragalactic sky is dominated by blazars, radio-loud active galactic nuclei with a relativistic jet pointing towards the Earth. Blazars show variability that can be quite exceptional both in terms of flux (orders of magnitude of brightening) and time (down to the minute timescale). This bright flaring activity contains key information on the physics of particle acceleration and photon production in the emitting region, as well as the structure and physical properties of the jet itself. The TeV band is accessed from the ground by Cherenkov telescopes that image the pair cascade triggered by the interaction of the gamma ray with the Earth's atmosphere. The Cherenkov Telescope Array (CTA) represents the upcoming generation of imaging atmospheric Cherenkov telescopes, with a significantly higher sensitivity and larger energy coverage with respect to current instruments. It will thus provide us with unprecedented statistics on blazar light-curves and spectra. In this contribution we present the results from realistic simulations of CTA observations of bright blazar flares, taking as input state-of-the-art numerical simulations of blazar emission models and including all relevant observational constraints.