Restrictive relative clauses identify and particularize the noun they modify, and the sentence would be incomplete without them: The zebra which the lion picked on was clearly sick. They can be introduced by the relative pronouns who, whom, whose or which, or by that: The zebra that the lion picked on was clearly sick. They can also be used without a relative pronoun: The zebra the lion picked on was clearly sick. You do not put a comma before and after them.
Non-restrictive relative clauses merely give additional information about the noun, which is dispensable: The zebra, which lives in southern Africa, is related to the horse. They can only be introduced by who, whom, whose and which, never by that. You generally put a comma before a non-restrictive relative clause (and after it, if it does not end the sentence).
There is a third sort of relative clause, which modifies not a noun but a whole clause: They can't come after all, which is a shame. It can only be introduced by which.
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