There is now strong evidence that dark energy comprises 70% of the density of the Universe and drives its present acceleration. Is this dark energy Einstein's cosmological constant (which he famously called his "greatest mistake") or is it an exotic new form of matter called quintessence?
Many current and planned large-scale surveys mapping the positions of many millions of galaxies out to great distances will help to distinguish between these competing scenarios. Detailed three dimensional maps of the Universe will provide the new frontier for testing cosmological theories.
What is the dark matter that makes up about 25% of the Universe and which holds together galaxies? According to some popular extensions of the standard model of particle physics, the dark mateer is composed of "superparticles", an idea which is being tested in CERN at the Large Hadron Collider. The quest for dark matter continues in many direct detection experiments, as well as possible beyond LHC with the proposed International Linear Collider.
These experimentals will also offer insight as to why there is vastly more ordinary matter than antimatter.