Numerical relativity has made big strides over the last decade. A number of
problems that have plagued the field for years have now been mostly solved.
This progress has transformed numerical relativity into a powerful tool to
explore fundamental problems in physics and astrophysics, and I present here
three representative examples. These "three little pieces" reflect a personal
choice and describe work that I am particularly familiar with. However, many
more examples could be made.Comment: 42 pages, 11 figures. Plenary talk at "Relativity and Gravitation:
100 Years after Einstein in Prague", June 25 - 29, 2012, Prague, Czech
Republic. To appear in the Proceedings (Edition Open Access). Collects
results appeared in journal articles [72,73, 122-124
