Mu2e is an experiment under construction at Fermilab that will search for the coherent neutrinoless conversion of a muon into an electron in the field of an atomic nucleus. This is a charged-lepton flavour violating process, and its observation would be clear evidence of physics beyond the standard model. Mu2e's single-event sensitivity of $3\times 10^{-17}$ is 4 orders of magnitude better than previous experiments looking at this reaction, and indirectly probes energy scales beyond those envisioned for high-energy colliders. To achieve the high sensitivity requires a very intense but low-energy muon beam, a high-precision measurement of the conversion electron's momentum, and several key mechanisms to reduce background events. This work presents an overview of the experimental design and construction status, focusing on four "Big Deal" items which are particularly innovative or interesting.