XeTeX is a typesetting system which allows one to use Unicode within the TeX or LaTeX source, making it much easier to use any OpenType or TrueType font with LaTeX. XeTeX is available for all major platforms, it is a standard component of the complete TeX Live distribution, and can be used as a command line tool or via a graphical user interface. Its input file is assumed to be in UTF-8 encoding by default.
XeTeX works well with both LaTeX and ConTeXt macro packages. Its LaTeX counterpart is invoked as xelatex. It is usually used with the fontspec package, which provides a configurable interface for font selection, and allows complex font choices to be named and later reused.
XeTeX enables classicists best of two worlds: the typographic features offered by LaTeX together with Unicode representations and codes for polytonic Greek. For example, a text or a sentence could be pasted from a Unicode source directly into a .tex file, which would then be processed with XeTeX typesetting engine to produce e. g. a PDF document (see an example on Wikipedia).
Typesetting Greek in LaTeX with Babel and psgreek is therefore not the only way to use LaTeX for classical Greek.
A XeTeX mailing list is the place to ask questions about installing or using the system.
XeTeX has its Wikipedia page.
Some Unicode fonts containing polytonic Greek glyphs, which can be used for typesetting Greek with XeTeX, are Gentium, GFS Neohellenic, Old Standard TT.