Leptonic and semi-leptonic $D$ decays at BESIII contribute the most precise experimental measurement of $|V_{cs(d)}|$ and decay constants $f_{D_{(s)}}$ in the world based on 2.93 fb$^{-1}$ and $3.19~{\rm fb}^{-1}$ data taken at center-of-mass energies $\sqrt{s} = 3.773$ GeV and 4.178 GeV, respectively. The largest samples at the mass threshold of the charmed hadrons $D_{(s)}$ also provide chances to extract form factors of some semi-electronic decays for the first time and together with the semi-muonic decays we could understand lepton flavour universality better.