Two classes of non-linear guidance algorithms for lunar precision landing are presented. The development of such algorithms is motivated by the need of more stringent landing requirements imposed by future lunar mission architectures (e.g. the ability to land anywhere from a generic lunar orbit). The first class of guidance algorithms, called Optimal Sliding Guidance (OSG) laws, analytically determine the optimal acceleration command and augment it with a sliding mode to provide robustness against perturbations. The second class of guidance algorithms, called Multiple Sliding Surface Guidance (MSSG) laws, employs two interconnected sliding surfaces to track an on-board generated trajectory that drive the descending lander to the desired location at the desired velocity. For both guidance algorithms, which are proven to be globally stable, a set of Monte Carlo simulations have been executed to verify their performances. Both algorithms perform very well, i.e. they exhibit precision a with very low guidance residual errors on the desired target point above the lunar surface. Overall, MSSG shows slightly better performances with two drawbacks: 1) it needs more propellant mass and 2) it requires a higher frequency guidance loop (greater or equal than 100 Hz). The latter it imposes more challenging requirements on the design of the lander avionics system. Conversely, OSG tends to behave in a smoother fashion with excellent landing performance, lower guidance cycle frequency (10 Hz) and less propellant mass. Importantly, MSSG may be employed as real-time guidance scheme to track trajectory generated by more conventional, Apollo-like targeting algorithms.