The astrophysical and cosmological evidence for dark matter is both impressive and compelling. What is perhaps the most striking are the multiple lines of evidence which point to the need for dark matter. Elemental abundances from Big Bang Nucleosynthesis and fundamental anisotropies in the Cosmic Microwave Background Radiation both predict very similar baryon (ordinary matter) abundances, yet each describes a completely separate era in the history of the universe in which very different physical processes are occurring. Dark matter is necessary to both describe galaxies and clusters of galaxies, and is a necessary ingredient in the formation of large scale structure. It is this concordance of evidence that makes dark matter more than just a "fudge-factor"; although strange and unexpected, dark matter seems to be a fundamental and necessary component of our universe.
Although the composition and nature of dark matter is still unknown, theories like Supersymmetry or Kaluza-Klein theories of extra dimensions provide solid frameworks for attempting to understand dark matter. Of all of the particle candidates for dark matter, perhaps the best motivated is the neutralino. It is a typical WIMP: electrically neutral, weakly interacting, and massive, and through statistical mechanics in the early universe we can calculate abundances for the neutralino today which are consistent with it acting as the dark matter. Other exotic candidates for dark matter exist from axions to Q-balls to WIMPzillas. However outlandish the candidate, the hunt for dark matter continues. The Large Hadron Collider at CERN will begin collisions at 3.5 TeV per beam in 2009-2010, ramping up to 7 TeV per beam most likely in 2011 and beyond, and will search for indications of supersymmetry and dark matter. Indirect searches continue to hunt for gamma rays and antimatter which might provide evidence for dark matter; the current controversy between PAMELA and ATIC and FERMI and HESS results demonstrate the advances and challenges in indirect detection. And finally, direct detection experiments continue to set more stringent limits on neutralino and WIMP scattering cross sections; these limits, as new technology is applied, are set to improve dramatically in the next decade with experiments like Super CDMS, GENIUS, and ZEPLIN IV.
Dark matter, of course, is not completely understood and faces challenges. The primary challenge is that it remains undetected in the laboratory. However, another crucial challenge for dark matter is that it seems to possess too much power on small scales (~ 1 - 1000 kpc). Numerical simulations of the formation of dark matter halos were performed by Klypin et al. and show that, to explain the average velocity dispersions for the Milky Way and Andromeda, there should be five times more dark matter satellites (dwarf galaxies with a very small ordinary matter content) with circular velocity > 10-20 km/s and mass > 3 × 108 M within a 570 kpc radius than have been detected.  In other words, although dark matter is crucial in forming structure, current models form too much structure. Another study, from B. Moore et al., shows that dark matter models produce more steeply rising rotation curves than we see in many low surface brightness galaxies, again suggesting that simulations produce an overabundance of dark matter.  One possible solution to this dilemma is to force dark matter to decay at the present time which "successfully lowers the concentration of dark matter in dwarf galaxies as well as in large galaxies like our own at low redshift, while simultaneously retaining the virtues of the CDM model."  Although important to consider, these challenges faced by dark matter are dwarfed by the compelling evidence for the necessity of dark matter along with its successes in explaining our universe. What makes this field so rich and vibrant is that work and research continue, and these challenges will lead to deeper understanding in the future.
Dark matter is an opportunity to learn more about the fundamental order of the universe. Dark matter provides a tantalizing glimpse beyond the highly successful standard model of particle physics; the discovery of neutralinos would prove the validity of supersymmetry and help bridge the "desert" between the electroweak and the Planck scales. But ultimately, we look at dark matter as a mystery, one which will hopefully inspire physics and astronomy students in and out of the classroom. As Einstein said, "The most beautiful thing we can experience is the mysterious. It is the source of all true art and all science."
K.G. and G.D. would like to acknowledge support from the NASA Nebraska Space Consortium through grant NNG05GJ03H.