We typically think of structures as systems that are stable, sturdy and whose properties are fixed in time (or change over very slow time scales). In the first part of this talk, I will illustrate the dynamics of an unstable cantilever beam with time-modulated properties. We engineer our system so that it switches between a first unstable state, with negative stiffness and positive damping and a second unstable state with positive stiffness and negative damping, while maintaining an unstable average. We show that, despite the absence of any stable feature or feedback, this unstable structure can be passively stabilized for narrow ranges of switching periods. In the second part of the talk, I will further illustrate how to leverage structural instabilities to design systems that exhibit interesting functionalities like programmable multistability and mechanical memory.