Recent technological advances have made it possible to develop computers that are extremely fast and efficient for numerical computations.  However, these computers lack the abilities of humans and animals in processing cognitive information acquired by natural sensors.  For example, the human brain routinely performs tasks like recognizing a face in an unfamiliar crowd in 100-200 ms whereas a computer can take days to accomplish a task of lesser complexity.  The use of fuzzy logic and neural networks can emulate the desirable computing aspects found in humans and animals.  Engineers and scientists have had many remarkable accomplishments such as putting people on the moon and returning them safely to Earth, sending spacecraft to the far reaches of the solar system, sending rovers to explore the surface of Mars, exploring the oceans depths, designing computers that can perform billions of computations per second, developing the nuclear bomb, mapping the human genome, and constructing a scanning tunneling microscope that can move individual atoms.  But alongside many outstanding achievements using unintelligent systems, there have been many abysmal failures that include modeling the behavior of physical, biological, economic, political, and social systems.  Engineers have been unable to develop technology that can decipher sloppy handwriting, recognize oral speech as well as a human can, translate between languages as well as a human interpreter can, drive a car in heavy traffic as well as a human can, walk with the agility of a human or animal, replace the combat infantry soldier, determine the veracity of a statement by a human subject with an acceptable degree of accuracy, replace judges and juries, summarize a complicated document, and explain poetry or song lyrics.  These remaining challenges and many more can benefit from fuzzy logic and neural networks.