Look up at the night sky - what do you see? All but a tiny fraction of the light that you see (and that being the light reflected off of planets and moons) is directly from stars. This is what astronomers study and cosmologists measure. However, the sum total mass of what we can see appears to only be a small fraction of the mass out there.

There are two ways to detect matter in the cosmos - seeing it directly (as with the light) or observing its effect upon light. Direct observation is the oldest and has been performed since the dawn of astronomy. More advanced telescopes have enabled astronomers to see smaller objects and objects further away - be it with the Hubble Space Telescope or with the giant radar dish of Arecibo. And yet, there are some things still to dim to see.

Recently, extra-solar planets have been discovered - not through direct observation, but rather by observing the gravitational tug of a planet (that which cannot be seen today) on a star (something that can be seen).

This brings us to dark matter. In the 1930s astronomers (primarily the Swiss astronomer Fritz Zwicky) were looking at galaxies and found that the vast majority of galaxies are clumped together in great clusters and along chains rather than stand in vast empty expanses. Looking at both the velocities galaxies traveling within the cluster and the mass of the galaxies, they were in for a shock - the velocities were off by an order or two of magnitude from what was expected with the estimated mass of the galaxies - traveling 10x to 100x faster than expected.

While good evidence of something strange, the velocity of galaxies with respect to clusters of galaxies has problems. It is difficult to determine if a galaxy is gravitationally bound to the cluster, sailing through, or is just a foreground galaxy.

Stronger evidence for dark matter came in the 1970s when the velocity of stars within a galaxy were examined. Just as planets spin around the star, so do stars spin around the center of the galaxy. These follow clearly from Kepler's Laws in which the rotational velocity of a body around the center depends only upon the distance to the center and the mass contained within the orbit.

With planets, this is clearly seen - The Earth takes 365 days to go around the sun, while Mars takes 687, Jupiter takes 4332, and Mercury zips around the sun every 88 days. With a galaxy, one would expect the stars near the center of the galaxy to be zipping around rapidly, while the stars at the edge to be moving very slowly. This is not the case - it turns out that the stars at the edges of the galaxy are moving much faster than they should be if the vast majority of the mass of a galaxy is at the center (like it appears to be). One expects the orbital velocity of stars to drop off rather than level off.

    Expected          |     Observed
s ^                   | s ^
p | .                 | p |      . . . .
e |  .                | e |   .
e |   .               | e |  .
d |     .             | d | . 
  |       . . .       |   | .
  +-------------->    |   +-------------->
    radius                  radius

While the spiral galaxies are the best evidence to date of dark matter, there is evidence also with star velocity in globular clusters, elliptical and dwarf galaxies (such as Sagittarius DEG).

The amount of mass in the universe is of interest to cosmologists in trying to determine the ultimate fate of the universe. Cosmologists have a value called Omega that relates to the total density of mass within the universe. If Omega is greater than 1, the universe is open - if it is less than one it is flat. At the precise balance of exactly 1, the universe is balanced between the two.

Taking all the visible matter in the universe into account gives an Omega value of 0.05 - stating that the universe should be flying apart. It more closely appears that the omega is close to 1, if not exactly one (though some put it at 0.4). This gives us the range from 80% - 95% of the mass in the universe is not seen.

There are many theories as to what dark matter is - some ordinary, some exotic.

Planets
While the earth isn't that massive, Jupiter gets up there - one theory is that of a lot of Jupiters could be some portion of the dark matter. Unfortunately there are some problems with this. The first is that planets only form around stars and then appear to only make a few percent of the mass of a solar system. Furthermore, when one looks at the Big Bang Nucleosynthesis it states that the vast majority of the normal matter (baryonic matter) within the universe is in the form of Hydrogen and Helium - there just isn't enough matter for planets to make up the dark matter. Furthermore, the BBN predicts the total amount of baryonic matter in the universe can only make Omega get up to about 0.2 (0.2 is the high estimate - it is often placed at 0.1).
Burned out and non-luminous stars
From Jupiter on up there is a range of almost stars called Brown Dwarfs (about 10x more massive than Jupiter). While these stars are not massive enough to produce light, they do exist hand have been detected. Likewise there are the cores of stars called White Dwarfs. These two stars are expected to be the most common stars in the universe and are barely detectable when nearby. However, the BBN still predicts that there isn't enough normal matter in the universe to make up for the Omega. These are often called MACHOs standing for Massive Compact Halo Objects.
Black Holes
Black holes range from stellar mass to super-massive. These are often invoked as candidates for dark matter. Quiet super-massive black holes (as opposed to their noisier kin in galactic centers and quasars) are very hard to detect, emitting only a tiny fraction (10^-11 of the rest mass).
At the other end of the spectrum is the exotic very small matter that may permeate the universe. While not as easily understood, this appears to be the case for what dark matter is - the Big Bang Nucleosynthesis indicates that normal matter can only account for Omega of to 0.2 - only accounting for at most 50% of the lowest estimate for Omega and only 20% of the critical value.
Neutrinos (hot dark matter)
Neutrinos were produced in staggering numbers in the early universe to the point at which the universe is thought to be saturated with them. Neutrinos are believed to account for 1.7 Kelvin of the 2.7 Kelvin cosmic background radiation. If neutrinos have mass (which it is believed they do) they can make a substantial impact on the value of Omega. However, these particles cannot account for all the dark matter - dwarf galaxies seem to have a much higher mass density than can be accounted for by neutrinos which would necessitate at least two different kinds of dark matter - one for low mass galaxies and another for more classical galaxies.
WIMPs (cold dark matter)
WIMPs make up a wide array of dark matter candidates. These particles have two qualities to them - Weakly Interacting and Massive Particles (thus the name wimps). These particles were believed to be created in the early universe (thus the statement "It takes GUTs to have WIMPs" refering to the Grand Unified Theory).
Others
There are other postulated particles that are allowed by the current theories - photinos which are cousin to photons but have a mass of 10x to 100x of a proton. Axions (a rather light particle theorized by quantum chromodynamics) and quark nuggets made up of strange quarks.

By no means do all astronomers agree with dark matter - which is still only a hypothesis (though a very strong one). One very distinct possibility is that we do not understand gravity properly. This lack of understanding can range from a non-zero Cosmological Constant to a modification of how gravity works at very low acceleration (more about this can be read at MOND and the Pioneer space probe acceleration anomaly).

The question is - what is it that accounts for what we see. Until a better theory comes along, Dark matter is one of the better explanations for why the universe is the way it is.


http://www.shef.ac.uk/uni/academic/N-Q/phys/research/pa/
http://nedwww.ipac.caltech.edu/level5/Sept01/Carr/Carr_contents.html
http://www.astro.princeton.edu/~dns/MAP/Bahcall/final.html
http://home.earthlink.net/~jjwhitt/DrX2/DarkMatter.html
http://zebu.uoregon.edu/~js/ast123/lectures/lec25.html
http://www.astro.queensu.ca/~dursi/dm-tutorial/