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 (lambda) 0.6-2 mm and redshift distributions at 0.1-2 mm, agree well. At the bright end (greater than or similar to 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) lambda = 0.85-2 mm-selected galaxies at z less than or similar to 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 S-0.85mm greater than or similar to 0.01 mJy. We predict SMG's disks contribute significantly (negligibly) to the rest-frame UV (IR). We investigate the 0 1 mJy lambda = 0.85-2 mm-selected galaxies finding their: (i) stellar masses are > 10(10.2) M-circle dot, with the 2mm ones tracing the most massive galaxies (> 10(11) M-circle dot); (ii) specific star formation rates (SFR) are mildly (approximate to 3-10 times) above the main sequence (MS); (iii) host halo masses are greater than or similar to 10(12.3) M-circle dot, with 2 mm galaxies tracing the most massive haloes (protoclusters); (iv) SMGs have lower dust masses (approximate to 10(8) M-circle dot), higher dust temperatures (approximate to 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 less than or similar to 1 kpc at z = 4; and (vi) the carbon monoxide line spectra of S-0.85mm greater than or similar to 1 mJy sources peak at 4 -> 3. Finally, we study the contribution of SMGs to the molecular gas and cosmic SFR density at 0 1 mJy sources make a negligible contribution at z greater than or similar to 3 and 5, respectively, suggesting current observations have unveiled the majority of the SF at 0