We consider possible applications of temporal superoscillatory optical signals.
First we discuss the delivery of a super-oscillatory optical signal through a medium with an
absorbing resonance at the super-oscillation frequency. While a regular signal oscillating
at the absorption resonance frequency would be completely absorbed after a few
absorption lengths, it is found that the superoscillation undergoes quasi-periodic revivals
over optically thick distances. In the second part of the talk we present experimental
results where the use of a superoscillating optical beat breaks the optical temporal   
Fourier resolution limit by an unprecedented 75%. Such superoscillatory beats can
substantially increase the temporal resolution of light-driven measurement and control
processes.