Searching for DOM elements

From the site http://javascript.info/tutorial/searching-elements-dom we get this summary

There are 5 main ways of querying DOM:

1. getElementById
2. getElementsByTagName
3. getElementsByName
4. getElementsByClassName (except IE<9)
5. querySelector (except IE<8 and IE8 in compat mode)

All of them can search inside any other element. All of them excepts the last one return live collections.

XPath is kind-of supported in most browsers, but very rarely used.