  We consider the phenomenological signatures of Simplified Models of
Flavourful Leptoquarks, whose Beyond-the-Standard Model (SM) couplings to
fermion generations occur via textures that are well motivated from a broad
class of ultraviolet flavour models (which we briefly review). We place
particular emphasis on the study of the vector leptoquark $\Delta_\mu$ with
assignments $\left({\bf{3}}, {\bf{1}}, 2/3 \right)$ under the SM's gauge
symmetry, $SU(3)_C \times SU(2)_L \times U(1)_Y$, which has the tantalising
possibility of explaining both $\mathcal{R}_{K^{(\star)}}$ and
$\mathcal{R}_{D^{(\star)}}$ anomalies. Upon performing global likelihood scans
of the leptoquark's coupling parameter space, focusing in particular on models
with tree-level couplings to a single charged lepton species, we then provide
confidence intervals and benchmark points preferred by low(er)-energy flavour
data. Finally, we use these constraints to further evaluate the (promising)
Large Hadron Collider (LHC) detection prospects of pairs of $\tau$-flavoured
$\Delta_\mu$, through their distinct (a)symmetric decay channels. Namely, we
consider direct third-generation leptoquark and jets plus missing-energy
searches at the LHC, which we find to be complementary. Depending on the
simplified model under consideration, the direct searches constrain the
$\Delta_\mu$ mass up to 1500-1770 GeV when the branching fraction of
$\Delta_\mu$ is entirely to third-generation quarks (but are significantly
reduced with decreased branching ratios to the third generation), whereas the
missing-energy searches constrain the mass up to 1150-1700 GeV while being
largely insensitive to the third-generation branching fraction.
