This paper reviews different approaches for explaining body sway while quiet standing that directly address the instability of the human inverted pendulum. We argue that both stiffness control [Winter, D. A., Patla, A. E., Riedtyk, S., & Ishac, M. (2001). Ankle muscle stiffness in the control of balance during quiet standing. Journal of Neurophysiology, 85, 2630-2633] and continuous feedback control by means of a PID (Proportional, Integral, Derivative) mechanism [Peterka, R. J. (2000). Postural control model interpretation of stabilogram diffusion analysis. Biological Cybernetics, 83, 335-343.] can guarantee asymptotic stability of controlled posture at the expense of unrealistic assumptions: the level of intrinsic muscle stiffness in the former case, and the level of background noise in the latter, which also determines an unrealistic level of jerkiness in the sway. We show that the decomposition of the control action into a slow and a fast component (rambling and trembling, respectively, as proposed by [Zatsiorsky, V. M., & Duarte, M. (1999). Instant equilibrium point and its migration in standing tasks: Rambling and trembling components of the stabilogram. Motor Control, 4, 185-200; Zatsiorsky, V. M., & Duarte, M. (2000). Rambling and trembling in quiet standing. Motor Control, 4, 185-200.]) is useful but must be modified in order to take into account that rambling is not a stable equilibrium trajectory. We address the possibility of a form of stability weaker than asymptotic stability in light of the intermittent stabilization mechanism outlined by [Loram, I. D., & Lakie, M. (2002a). Human balancing of an inverted pendulum: position control by small, ballistic-like, throw and catch movements. Journal of Physiology, 540, 1111-1124.], and propose an indicator of intermittent stabilization that is related to the phase portrait of the human inverted pendulum. This indicator provides a further argument against the plausibility of PID-like control mechanisms. Finally, we draw attention to the sliding mode control theory that provides a useful theoretical framework for formulating realistic intermittent, stabilization models.