Austrian economics (or the Austrian school of economics) is a school of economic thought that eschews mathematical modeling and empirical testing in favor of a narrative approach termed "praxeology."
As the claims of Austrian economists are difficult to verify through empirical testing (and the same economists openly admit to it), it is generally considered to be a heterodox approach or outright pseudoscience. Austrian arguments as to why statistical methods cannot adequately describe human behavior can seem intuitively compelling, but they fail to provide the mathematical proof demonstrating why normally unbiased estimates suddenly become biased simply because they are dealing with people who make decisions. In this sense, the Austrian school is to economics as Psychoanalysis, a certain other Austrian school was to psychology.
Perhaps one reason supporters of the Austrian School are so uncomfortable with empiricism is that Austrian economists are more interested in defending the political ideology of libertarianism than they are in advancing economic understanding, and rigorous testing can sometimes undermine deeply held political beliefs. 
Many economists are critical of the current-day Austrian School and feel it rejects many types of economic analysis that mainstream economic theory accepts.
History and development
The Austrian School originated in late-19th and early- 20th Century Vienna with the work of Carl Menger, Eugen von Böhm-Bawerk, Friedrich von Wieser, and others. It now includes Murray Rothbard, Ludwig von Mises, possibly Friedrich Hayek, Milton Friedman, Ayn Rand and others. 
- "Statistical Malfeasance and Interpreting Economic Phenomena", Mises Institute
- "What is Austrian Economics?", Mises Institute
- Caplan, Bryan. "Why I Am Not an Austrian Economist", George Mason University
- "Austrian Economics and Classical Liberalism", Mises Institute
- Incidentally Marxists are also uncomfortable with empiricism because it can undermine their faith held beliefs.
- Why I Am Not an Austrian Economist