Online LaTeX is still LaTeX -- primarily destined for the print-based world. Whether the compiler is local or online, LaTeX is still weirdly out of place in a web-first research world. Getting LaTeX to look good on the web is a long-lasting problem!  

The two pure online LaTeX compilers out there are ShareLaTeX and Overleaf. The two options are fairly interchangeable with some minor differences. Authorea is an alternative to ShareLaTeX and Overleaf that is intended for use by all researchers rather than just LaTeX writers. Authorea is the only web-based writing environment for researchers that supports LaTeX, markdown, and richtext in the same place -- and renders all typesetting to beautiful HTML5 in the browser.