Thermonuclear fusion has the potential to provide safe, cheap and virtually inexhaustible energy for future generations of mankind. Fusion is the energy source of our sun and for many decades, physicists have pursued various strategies to harness fusion reactions in a controlled way here on Earth. Perhaps the most promising of these schemes is a concept known as direct-drive inertial-confinement fusion (ICF) in which intense laser light symmetrically implodes BB-sized pellets containing frozen isotopes of hydrogen, rapidly compressing this fuel to the extreme temperatures and densities required for fusion to occur. While the development of a commercial fusion reactor is still likely decades away, significant progress has been made in recent years in our understanding of many of the phenomena that have thwarted the realization of successful fusion thus far, particularly hydrodynamic and laser-plasma instabilities. In this presentation, I will discuss the fundamental principles of ICF and present numerical simulations that help to elucidate the physics underlying two of these deleterious processes: the ablative Rayleigh-Taylor instability and cross-beam energy transfer. I will also outline some possible mitigation strategies for suppressing such instabilities in an ICF implosion, including the use of deep-UV laser wavelengths, multi-terahertz laser bandwidths and thin, “high-Z” overcoats — each of which is presently an active area of fusion research at the U.S. Naval Research Laboratory.