Fabrication of optoelectronic devices from III-V nitrides and operating in the blue and ultraviolet regions of the spectrum has been a goal of many groups practically since the first infrared and red devices were produced. While much of the original research on these materials centered around films with the wurtzite structure, the zinc blende structure nitrides have been receiving increasing interest. Recent results from several groups around the world have successfully addressed some of the traditional problems associated with growth of all these materials. Chemical vapor deposition (CVD) has been the most common technique for nitride growth and continues to be very successful. However, many researchers, including those growing III-V nitrides, have turned to molecular beam epitaxy (MBE) for its important advantages in purity and in situ analytical capabilities. This paper will review the recent developments in MBE growth of aluminum nitride, gallium nitride, and their heterostructures.