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 absorbedCOMPPS model yielding as best fit parameters a column density ofNH = (2.09 ± 0.05) × 1022cm−2, a blackbody seed photon temperaturekTbb, seedof 0.64 ± 0.02 keV, electron temperaturekTe = 38.8 ± 1.2 keV and Thomson optical depthτT = 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.