The objective of humanoid navigation is to plan the global locomotion path for humanoid robots in complex global environments. It is different from wheeled mobile robot navigation because of the biped's unique abilities to step upon/over obstacles and the stability requirement is difficult. Sampling-based footstep planning that considers the aforementioned characteristics is a goal-directed navigation approach for humanoid robots. This paper will describe two footstep planning approaches, including our improvements on the previous deterministic sampling-based approach and the newly proposed randomized sampling-based approach. Numerical experiments are also given to verify the feasibility and planning performance of the two approaches.