The chapter describes damage prognosis techniques in the context of structural health monitoring for aerospace materials, and illustrates the efficacy of the proposed methods using fatigue data from a graphite-epoxy composite coupon. Prognostics is a core element in health management sciences which aims to predict remaining useful lifetime of the systems or components through estimation of their future health state based on partial knowledge about the current health state and future system usage. The methods shown in this chapter use a physicsbased modeling approach whereby the time-dependent behavior of the damaged material is idealized via mathematical equations that rely on physical principles. Rigorous mathematical tools are used to estimate the uncertainty associated with the prediction process. Information stemming from these predictions is usable in an operational context for informed decisions about safety and maintenance, amongst others.