IGR J17591-2342 is an accreting millisecond X-ray pulsar, discovered with INTEGRAL, which went into outburst around July 21, 2018. To better understand the physics acting in these systems during the outburst episode, we performed detailed temporal-, timing-, and spectral analyses across the 0.3-300 keV band using data from NICER, XMM-Newton, NuSTAR, and INTEGRAL. The hard X-ray 20-60 keV outburst profile covering ∼85 days is composed of four flares. Over the course of the maximum of the last flare, we discovered a type-I thermonuclear burst in INTEGRAL JEM-X data, posing constraints on the source distance. We derived a distance of 7.6 ± 0.7 kpc, adopting Eddington-limited photospheric radius expansion and assuming anisotropic emission. In the timing analysis, using all NICER 1-10 keV monitoring data, we observed a rather complex set of behaviours starting with a spin-up period (MJD 58345-58364), followed by a frequency drop (MJD 58364-58370), an episode of constant frequency (MJD 58370-58383), concluded by irregular behaviour till the end of the outburst. The 1-50 keV phase distributions of the pulsed emission, detected up to ∼120 keV using INTEGRAL ISGRI data, was decomposed in three Fourier harmonics showing that the pulsed fraction of the fundamental increases from ∼10% to ∼17% going from ∼1.5 to ∼4 keV, while the harder photons arrive earlier than the soft photons for energies ≲10 keV. The total emission spectrum of IGR J17591-2342 across the 0.3-150 keV band could adequately be fitted in terms of an absorbed COMPPS model yielding as best fit parameters a column density of NH = (2.09 ± 0.05) × 1022 cm-2, a blackbody seed photon temperature kTbb, seed of 0.64 ± 0.02 keV, electron temperature kTe = 38.8 ± 1.2 keV and Thomson optical depth τT = 1.59 ± 0.04. The fit normalisation results in an emission area radius of 11.3 ± 0.5 km adopting a distance of 7.6 kpc. Finally, the results are discussed within the framework of accretion physics- and X-ray thermonuclear burst theory.
