These units have the advantage of simplifying many equations in physics by removing conversion factors; for example, Einstein's famous equation becomes simply . For this reason, the units are popular in quantum gravity research.
However, they are too small for practical use, unless prefixed with large powers of ten. They also suffer from uncertainties in the measurement of some of the constants on which they are based, especially of the gravitational constant G.
The Planck units are:
The NIST (National Institute of Standards and Technology) website is a convenient source of data on the commonly-recognized constants, including Planck units.
Max Planck first listed his set of units (and gave values for them remarkably close to those used today) in May of 1899 in a paper presented to the Prussian Academy of Sciences.
Max Planck: 'Über irreversible Strahlungsvorgänge'. Sitzungsberichte der Preußischen Akademie der Wissenschaften, vol. 5, p. 479 (1899).
At the time he presented the units, quantum mechanics had not been invented. He himself had not yet discovered the theory of blackbody radiation (first published December 1900) in which the constant h made its first appearance and for which Planck was later awarded the Nobel prize. The relevant parts of Planck's 1899 paper leave some confusion as to how he managed to come up with the units of time, length, mass, temperature etc. which today we define using h-bar and motivate by references to quantum physics before things like h-bar and quantum physics were known. Here's a quote from the 1899 paper that gives an idea of how Planck thought about the set of units.
Max Planck's creation of the natural units
See also