Fundamental Constants

Fundamental Constants a preprint by Frank Wilczek, has a nice discussion of the fundamental constants of physics as well as systems of units.
There's a nice quote attributed to Einstein:

I would like to state a theorem which at present can not be based upon anything more than upon a faith in the simplicity, i.e., intelligibility, of nature: there are no arbitrary constants ... that is to say, nature is so constituted that it is possible logically to lay down such strongly determined laws that within these laws only rationally completely determined constants occur (not constants, therefore, whose numerical value could be changed without destroying the theory).

Gravity poses some problems:

Straightforward estimation suggests that empty space should weigh several orders of magnitude of orders of magnitude (no misprint here!) more than it does. It “should” be much denser than a neutron star, for example. The expected energy of empty space acts like dark energy, with negative pressure, but far more is expected than is observed.

And there are other less than pretty parts as well:

The flavor/Higgs sector of the standard model is, by a wide margin, its least satisfactory part. Whether judged by the large number of independent parameters or by the small number of powerful ideas it contains, our theory of this sector does not attain the same level as we’ve reached in the other sectors. This part truly deserves to be called a “model” rather than a “theory”.