Quantum mechanics predicts that the state of a harmonic oscillator with the least energy -- the ground state -- is not one of absolute rest. Macroscopic mechanical oscillators appear to be oblivious to this prediction -- partly owing to the challenge of preparing them in sufficiently low energy pure states, and equally due to the difficulty in resolving low energy states with sufficient precision. With recent developments in the field of cavity optomechanics -- wherein mechanical oscillators are strongly coupled to electromagnetic cavities -- it has become possible to experimentally address these challenges. Our group at EPFL has pioneered some of these developments with a view towards studying the limits imposed by quantum mechanics on the ability to measure and control nanomechanical oscillators. Using a cryogenic cavity-enhanced interferometer, we have recently demonstrated the ability to resolve the motion of a glass nanostring with an imprecision 40 dB smaller than its zero-point motion. The resulting back-action of the measurement is commensurate with the prediction of the uncertainty principle, resulting in an imprecision-back-action product of 5 hbar/2. The continuous record of this highly efficient measurement is used in a feedback loop to cool the oscillator close to its ground state, thereby cancelling measurement back-action -- an example of quantum feedback. We have witnessed the zero-point motion of the cold oscillator via quantum correlations induced by it on the optical field exiting the interferometer. Finally, I will discuss how a specific manifestation of such quantum correlations -- squeezing of the optical field -- can be used for quantum-enhanced force detection even at room temperature.