BeautifulSoup: what’s the difference between ‘lxml’ and ‘html.parser’ and ‘html5lib’ parsers?

From the docs‘s summarized table of advantages and disadvantages:

1. html.parser – BeautifulSoup(markup, "html.parser")

   • Advantages: Batteries included, Decent speed, Lenient (as of Python 2.7.3 and 3.2.)

   • Disadvantages: Not very lenient (before Python 2.7.3 or 3.2.2)

2. lxml – BeautifulSoup(markup, "lxml")

   • Advantages: Very fast, Lenient

   • Disadvantages: External C dependency

3. html5lib – BeautifulSoup(markup, "html5lib")

   • Advantages: Extremely lenient, Parses pages the same way a web browser does, Creates valid HTML5

   • Disadvantages: Very slow, External Python dependency