We present an atlas of a sample of local (z < 0.1) LIRGs (10) and ULIRGs (7) covering the luminosity range log(L IR /L ) = 11.1−12.4. The atlas is based on near-infrared H (1.45−1.85 μm) and K-band (1.95−2.45 μm) VLT-SINFONI integral field spectroscopy (IFS). The atlas presents the ionised, partially ionised, and warm molecular gas two-dimensional flux distributions and kinematics over an FoV of ∼3 × 3 kpc (LIRGs) and ∼12 × 12 kpc (ULIRGs) and with average linear resolutions of ∼0.2 kpc and ∼0.9 kpc, respectively. The different phases of the gas show a wide morphological variety with the nucleus as the brightest Brγ source for ∼33% of the LIRGs and ∼71% of the ULIRGs, whereas all the LIRGs and ULIRGs have their maximum H 2 emission in their nuclear regions. In LIRGs, the ionised gas distribution is dominated by the emission from the star-forming rings or giant HII regions in the spiral arms. The Brγ and [FeII] line at 1.644 μm trace the same structures, although the emission peaks at different locations in some of the objects, and the [FeII] seems to be more extended and diffuse. The ULIRG subsample is at larger distances and contains mainly pre-coalescence interacting systems. Although the peaks of the molecular gas emission and the continuum coincide in ∼71% of the ULIRGs, regions with intense Paα (Brγ) emission tracing luminous star-forming regions located at distances of 2−4 kpc away from the nucleus are also detected, usually associated with secondary nuclei or tidal tails. LIRGs have mean observed (i.e. uncorrected for internal extinction) SFR surface densities of about 0.4 to 0.9 M yr −1 kpc −2 over large areas (4−9 kpc 2 ) with peaks of about 2−2.5 M yr −1 kpc −2 in the smaller regions (0.16 kpc 2 ) associated with the nucleus of the galaxy or the brightest Brγ region. ULIRGs do have similar average SFR surface densities for the integrated emitting regions of ∼0.4 M yr −1 kpc −2 in somewhat larger areas (100−200 kpc 2 ) and for the Paα peak (∼2 M yr −1 kpc −2 in 4 kpc 2 ). The observed gas kinematics in LIRGs is primarily due to rotational motions around the centre of the galaxy, although local deviations associated with radial flows and/or regions of higher velocity dispersions are present. The ionised and molecular gas share the same kinematics (velocity field and velocity dispersion) to first order, showing slight differences in the velocity amplitudes (peak-to-peak) in some cases, whereas the average velocity dispersions are compatible within uncertainties. As expected, the kinematics of the ULIRG subsample is more complex, owing to the interacting nature of the objects of the sample.