Experiments in laser physics often require more comprehensive information about a beam than can be extracted from temporal and spatial profile measurements alone. In particular, the determination of irradiance and phase distribution at locations were measurement is difficult or even not feasible, e.g. near focus, meets high interest as those parameters limit the performance of a wide class of laser applications. Here we present Hartmann-Shack wavefront measurements and results of consecutive numerical beam propagation on laser beams of various complexity, reaching from HeNe fundamental mode beams with aberrations over high-energy q-switched Nd:YAG nanosecond pulses, KrF excimer laser beams to ultra-broadband laser pulses with a spectral bandwidth of >190 THz, which are produced by focusing amplified pulses from a 20 fs Ti:Sapphire oscillator-amplifier system into an Argon filled hollow fibre. Coherent propagation theory in combination with the Hartmann-Shack input data yields good agreement to measurement for the monochromatic coherent beams, whereas propagation of partial coherent beams requires information beyond Hartmann- Shack. Furthermore, measurements of the overall polychromatic Ti:Sapphire wavefront are faced to a couple of quasimonochromatic ones covering the whole spectrum. Incoherent superposition of the spectral components yields excellent agreement to the measured overall wavefront and the analysis of back-propagated spectral intensity distributions proof the spectral homogeneity of the beam at fibre output, showing that those beams can be sensed reliably by a single measurement. Drawbacks and opportunities of the Hartmann-Shack technique for means of propagation prediction of laser beams are discussed.