This is a subset of the tools I use for my research.

Stata, general purpose statistical package.

Julia, programming language geared towards technical computing.

Mathematica, high-level programming language.

Jupyter, interactive interface to many programming languages.

I also play with Python, R, MATLAB, and GAUSS.

If you are interested in technical computing in Economics, you can get an overview of the performance of different languages in this paper (updated here). Also, this website has a pretty cool section on choosing languages. This website provides tutorials for doing Econometrics in Julia. Another tutorial is available here. And here, here, and here you can find other applications in Economics and Econometrics. For performance computing, check here. If you are coming from MATLAB, you will find this useful. And this is useful in general.

I need to reorganize this page. In the meantime, here are some other useful links:

Econ-ML

DataFrames tutorial

JuliaDB tutorial

Parallel Computing in Econ

Jesús Fernández-Villaverde notes

Julia for Data Science

Julia Cookbook