Weak values were originally introduced by Aharanov, Albert and Vaidman for understanding the arrow of time in quantum mechanics. Weak values have recently proved useful in amplifying very small effects. I will introduce the ideas of weak values and discuss some of our recent experimental results in which we were able to observe a deflection of a laser beam of less than 1 picoradian (equivalent to measuring a deflection of the width of a hair at the distance of the moon). Perhaps more interestingly, the noise properties lead to a suppression of technical noise and an amplification of the signal to noise ratio to the optimal value for coherent states for standard beam deflection techniques. I will also discuss the use of weak values and precision deflection measurements for precision spectral and phase measurements.