Recent progress on lower hybrid current drive (LHCD) experiment and simulation towards steady-state (t ⩾ 3–5 × τr, where τr is the current relaxation time) regimes on Alcator C-Mod is presented. Highly non-inductive reversed shear plasmas are obtained with spontaneous generation of internal transport barriers at the density close to what is expected on ITER steady-state scenarios. Progress has been made to better understand and mitigate the unexpected degradation of LHCD efficiency at high densities, which poses an issue both for extending the non-inductive plasmas to advanced tokamak regimes (with a high bootstrap current fraction, fBS) on C-Mod and for predicting the performance of LHCD on future devices such as ITER. Several physics mechanisms that potentially contribute anomalous losses of LHCD power have been studied extensively. Numerical modelling of collisional absorption in cold scrape-off layer plasmas has been integrated into a ray-tracing code. The LHEAF full-wave code clarifies that full-wave effects move the power deposition profile closer to the separatrix than a calculation based on the WKB approximation, leading to a lower efficiency. Non-linear wave interactions were studied experimentally by LH wave spectral measurements using Langmuir probes, suggesting parametric decay instabilities to explain the remaining difference between experiments and simulations. An experimental demonstration of recovery of good LHCD efficiency at high densities is also reported. Improving the single pass absorption is proposed as a key to recover LHCD efficiency. A wave physics design of additional launcher (LH3) has been developed in order to demonstrate an improved LHCD performance by realizing high (∼80%) single pass absorption, in which the synergistic interaction in the velocity space with the existing launcher is maximized.