Examples

Given the string foobarbarfoo:

bar(?=bar)     finds the 1st bar ("bar" which has "bar" after it)
bar(?!bar)     finds the 2nd bar ("bar" which does not have "bar" after it)
(?<=foo)bar    finds the 1st bar ("bar" which has "foo" before it)
(?<!foo)bar    finds the 2nd bar ("bar" which does not have "foo" before it)

You can also combine them:

(?<=foo)bar(?=bar)    finds the 1st bar ("bar" with "foo" before it and "bar" after it)

Definitions

Look ahead positive (?=)

Find expression A where expression B follows:

A(?=B)

Look ahead negative (?!)

Find expression A where expression B does not follow:

A(?!B)

Look behind positive (?<=)

Find expression A where expression B precedes:

(?<=B)A

Look behind negative (?<!)

Find expression A where expression B does not precede:

(?<!B)A

Atomic groups (?>)

An atomic group exits a group and throws away alternative patterns after the first matched pattern inside the group (backtracking is disabled).