We present predictions for the clustering of galaxies selected by their emission at far infra-red (FIR) and sub-millimetre wavelengths. This includes the first predictions for the effect of clustering biases induced by the coarse angular resolution of single-dish telescopes at these wavelengths. We combine a new version of the GALFORM model of galaxy formation with a self-consistent model for calculating the absorption and re-emission of radiation by interstellar dust. Model galaxies selected at $850$ $mu$m reside in dark matter halos of mass $M_{rm halo}sim10^{11.5}-10^{12}$ $h^{-1}$ M$_{odot}$, independent of redshift (for $0.2lesssim zlesssim4$) or flux (for $0.25lesssim S_{850murm m}lesssim4$ mJy). At $zsim2.5$, the brightest galaxies ($S_{850murm m}>4$ mJy) exhibit a correlation length of $r_{0}=5.5_{-0.5}^{+0.3}$ $h^{-1}$ Mpc, consistent with observations. We show that these galaxies have descendants with stellar masses $M_{star}sim10^{11}$ $h^{-1}$ M$_{odot}$ occupying halos spanning a broad range in mass $M_{rm halo}sim10^{12}-10^{14}$ $h^{-1}$ M$_{odot}$. The FIR emissivity at shorter wavelengths ($250$, $350$ and $500$ $mu$m) is also dominated by galaxies in the halo mass range $M_{rm halo}sim10^{11.5}-10^{12}$ $h^{-1}$ M$_{odot}$, again independent of redshift (for $0.5lesssim zlesssim5$). We compare our predictions for the angular power spectrum of cosmic infra-red background anisotropies at these wavelengths with observations, finding agreement to within a factor of $sim2$ over all scales and wavelengths, an improvement over earli
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