Introduction to LaTeX Software 

LaTeX (pronounced lay-tech or lah-tech) is a markup language and document typesetting system. Developed by Leslie Lamport and originally released in 1985, the software has proliferated greatly since its release. It is distributed under a free and open source license, but there are numerous paid LaTeX software offerings  \cite{tex}.
Despite the lack of a unified style specification, LaTeX remains a standard for many academic publications. Especially those in areas like physics, astronomy, mathematics, and other technical fields. Despite the lack of a WYSIWYG interface (LaTeX source code is vastly different than rendered LaTeX), LaTeX remains popular for typesetting and publishing because of the professional outputs available via LaTeX software.

All LaTeX software originates from TeX

The progenitor of LaTeX is TeX, a typesetting system first introduced by computer scientist and mathematician Donald Knuth in 1978. TeX software was designed to make it easy to translate nonstandard characters to the computer. Also, to ensure that the results would be the same no matter where the content was viewed.
Now more than 30 years old, LaTeX remains one of the most popular tools out there for writing scientific and technical content. Authorea recently estimated that ~20% of scholarly articles are still written in LaTeX. This is surprising since LaTeX was developed in the pre-Internet era and was originally designed for a world in which document editors copied the paradigm of pen and paper. Today's leading document editors and LaTeX software are designed for a world in which content is shared and distributed on the web. As a result, the old model of page-based document editing is starting to look more and more obsolete.

Most popular LaTeX software

The most popular LaTeX software options today are compilers that run locally on a user's machine. Some example are the following:

Issues with LaTeX software

LaTeX was not created with the modern web in mind. It was created with physical pieces of paper in mind. Therefore, LaTeX software is suited to produce professional on-the-page results. It is ill-suited to produce professionally typeset web content. This has long been a frustration for many and there have been numerous attempts to convert LaTeX to HTML over the years. 

The future of LaTeX software on the web

Authorea provides the only web-based LaTeX environment that renders beautifully to HTML5 in the browser.

Further Reading

MathML on the Web, Please!