We thoroughly explore the properties of (sub)-millimetre (mm) selected galaxies (SMGs) in the shark semi-analytic model of galaxy formation. Compared to observations, the predicted number counts at wavelengths (λ) 0.6-2 mm and redshift distributions at 0.1-2 mm, agree well. At the bright end (≥1 mJy), shark galaxies are a mix of mergers and disc instabilities. These galaxies display a stacked far-ultraviolet (FUV)-to-far-infrared (FIR) spectrum that agrees well with observations. We predict that current optical/NIR surveys are deep enough to detect bright (>1 mJy) λ = 0.85-2 mm-selected galaxies at z ≲ 5, but too shallow to detect counterparts at higher redshift. A James Webb Space Telescope 10 000s survey should detect all counterparts for galaxies with S0.85mm ≳ 0.01 mJy. We predict SMG's disks contribute significantly (negligibly) to the rest-frame UV (IR). We investigate the 0 ≤ z ≤ 6 evolution of the intrinsic properties of >1 mJy λ = 0.85-2 mm-selected galaxies finding their: (i) stellar masses are > 1010.2, M⊙, with the 2 mm ones tracing the most massive galaxies (> 1011 M⊙); (ii) specific star formation rates (SFR) are mildly (≈3-10 times) above the main sequence (MS); (iii) host halo masses are > 1012.3, M⊙, with 2 mm galaxies tracing the most massive haloes (protoclusters); (iv) SMGs have lower dust masses (≈ 108 M⊙), higher dust temperatures (≈40-45 K) and higher rest-frame V-band attenuation (>1.5) than MS galaxies; (v) sizes decrease with redshift, from 4 kpc at z = 1 to ≲1 kpc at z = 4; and (vi) the carbon monoxide line spectra of S0.85mm ≳ 1 mJy sources peak at 4 → 3. Finally, we study the contribution of SMGs to the molecular gas and cosmic SFR density at 0 ≤ z ≤ 10, finding that >1 mJy sources make a negligible contribution at z ≳ 3 and 5, respectively, suggesting current observations have unveiled the majority of the SF at 0 ≤ z ≤ 10.