My dream is that Julia completely replaces Matlab. Until then:

• CompEcon. Old and not open-source, but useful.
• Chebfun . Powerful approach to solving functional equations
• Tomlab. Commerical matlab optimizer framework that has allows me to solve complicated problems. I typically use NPSOL and Knitro with auto-differentiation using MAD.

A few useful links for economists:

• Quantitative Economics Lectures and . A general purpose library (and textbook) using Julia and Python
• CompEcon wrapper around Basis Matrices
• BasisMatrices Basis matrices for orthogonal polynomials, collocation, etc.

For those trying to decide the right time to start Julia, consider watching github to see how radically it is going to change, and important breaking changes.

• Issues for 1.0 version