  Mechanical systems are ideal candidates for studying quantumbehavior of
macroscopic objects. To this end, a mechanical resonator has to be cooled to
its ground state and its position has to be measured with great accuracy.
Currently, various routes to reach these goals are being explored. In this
review, we discuss different techniques for sensitive position detection and we
give an overview of the cooling techniques that are being employed. The latter
include sideband cooling and active feedback cooling. The basic concepts that
are important when measuring on mechanical systems with high accuracy and/or at
very low temperatures, such as thermal and quantum noise, linear response
theory, and backaction, are explained. From this, the quantum limit on linear
position detection is obtained and the sensitivities that have been achieved in
recent opto and nanoelectromechanical experiments are compared to this limit.
The mechanical resonators that are used in the experiments range from
meter-sized gravitational wave detectors to nanomechanical systems that can
only be read out using mesoscopic devices such as single-electron transistors
or superconducting quantum interference devices. A special class of
nanomechanical systems are bottom-up fabricated carbon-based devices, which
have very high frequencies and yet a large zero-point motion, making them ideal
for reaching the quantum regime. The mechanics of some of the different
mechanical systems at the nanoscale is studied. We conclude this review with an
outlook of how state-of-the-art mechanical resonators can be improved to study
quantum {\it mechanics}.
