Context. The system of four planets discovered around the intermediate-mass star HR8799 offers a unique opportunity to test planet formation theories at large orbital radii and to probe the physics and chemistry at play in the atmospheres of self-luminous young (∼30 Myr) planets. We recently obtained new photometry of the four planets and low-resolution (R ∼ 30) spectra of HR8799 d and e with the SPHERE instrument (Paper III). Aims. In this paper (Paper IV), we aim to use these spectra and available photometry to determine how they compare to known objects, what the planet physical properties are, and how their atmospheres work. Methods. We compare the available spectra, photometry, and spectral energy distribution (SED) of the planets to field dwarfs and young companions. In addition, we use the extinction from corundum, silicate (enstatite and forsterite), or iron grains likely to form in the atmosphere of the planets to try to better understand empirically the peculiarity of their spectrophotometric properties. To conclude, we use three sets of atmospheric models (BT-SETTL14, Cloud-AE60, Exo-REM) to determine which ingredients are critically needed in the models to represent the SED of the objects, and to constrain their atmospheric parameters (T eff , log g, M/H). Results. We find that HR8799d and e properties are well reproduced by those of L6-L8 dusty dwarfs discovered in the field, among which some are candidate members of young nearby associations. No known object reproduces well the properties of planets b and c. Nevertheless, we find that the spectra and WISE photometry of peculiar and/or young early-T dwarfs reddened by submicron grains made of corundum, iron, enstatite, or forsterite successfully reproduce the SED of these planets. Our analysis confirms that only the Exo-REM models with thick clouds fit (within 2σ) the whole set of spectrophotometric datapoints available for HR8799 d and e for T eff = 1200 K, log g in the range 3.0−4.5, and M/H = +0.5. The models still fail to reproduce the SED of HR8799c and b. The determination of the metallicity, log g, and cloud thickness are degenerate. Conclusions. Our empirical analysis and atmospheric modelling show that an enhanced content in dust and decreased CIA of H 2 is certainly responsible for the deviation of the properties of the planet with respect to field dwarfs. The analysis suggests in addition that HR8799c and b have later spectral types than the two other planets, and therefore could both have lower masses.