Astrophysicists are working on various projects such as the likely age of the universe, the size of the observable universe, how long our sun will last before it exhausts its nuclear fuel, the commonness of black holes, what the universe looked like billions of years ago, and the way that matter is distributed across the observable universe.
One way astrophysicists are doing this is through the design and usage of various telescopes. They are observing the smallest of light variations of stars and exploring the physical properties inside stars. As more powerful telescopes are being designed, scientists are able to look further away (and thus further back in time) to discover and analyze exotic objects and states of matter. This has implications for how the universe will end, when this will happen, and what will happen next.
Researchers are combining observational, computational, and theoretical techniques to explore the properties of stars, galaxies, and the universe. This includes the physics behind astrophysical objects (eg. neutron stars, black holes, quasars), and the physics and structure of the universe on extragalactic scales.
Some researchers are studying our own Milky Way galaxy to determine the nature of the black hole at the center. These people are working with quantum physicists, astronomers, and engineers to determine the physical properties in the vicinity of the black hole, and what might lie beyond. Others are working on the premise that black holes may represent wormholes in space and time, and using this information to determine if time travel, or faster-than-light travel, is possible.
Many astrophysicists work with astronomers and physicists on a variety of collaborative projects, not necessarily involving astrophysics. See the articles on physics and astronomy for more information.