In the 20th century, many problems across all of physics were solved 
by perturbative methods which reduced them to harmonic oscillators.
Black holes are poised to play a similar role in the 21st century.  
They are at once both the simplest and the most complex objects in 
the physical world. They are maximally complex in that the number of possible 
microstates, or entropy, of a black hole is believed to saturate a  universal bound. They are maximally simple in that, according to Einstein's theory, they are a  featureless empty hole in space characterized only by mass, charge  and angular momentum.
Progress over the last decade in understanding the dual quantum  relation of simplicity and complexity embodied in black holes has  been successfully applied to problems in string theory, the  fundamental laws of nature,  astronomy, condensed matter, nuclear and  atomic physics.  In this lecture I will describe these developments.