Rock slope stability and rockfall are very interesting subjects, and traditionally involves terms like plane and wedge failure, joint friction angle, pore pressure, freeze-thaw. We also use terms like factor of safety and probability of failure. A term often missing in traditional slope stability is time: when will the slope fail, or how will the factor of safety change with time. If we monitor a large rock slope or hanging rock block using surveyed prisms or radar, when the slope is close to failure we can sometimes predict time of failure using inverse velocity techniques. But in such a rock slope or hanging block, what is changing with time that is causing the inverse velocity behavior? In this Jahns talk I will first of all briefly review traditional slope stability, including plane and wedge failure and the subjects of factor of safety, probability of failure, and the inverse velocity technique for predicting time-of-failure. I will then discuss two concepts that are central to the time dependence of rock failure: time-dependent crack growth and rock bridges. Rock bridges are intact sections along a discontinuity that must be broken in order for slope instability to occur. Rock bridges are often under high stress, and these bridges can fail due to time-dependent crack growth. Talking about these subjects requires discussing the complex subject of fracture mechanics, which I will do as carefully as I can (and with examples). I will show several interesting cases studies such as the example of rockfall in Yosemite where hanging blocks held up by intact rock bridges have been monitored using thermal imaging and the stability analyzed using fracture mechanics.