Defining relative clauses
Defining relative clauses give essential information about a noun.
1. My sister, who lives in London, is coming to Paris.
2. My sister who lives in London is coming to Paris.

In sentence 1, who lives in London is a non-defining relative clause. It gives extra non-essential information about the sister.

In sentence 2, it is a defining relative clause: I have more than one sister so I identify which sister I'm talking about.

In defining relative clauses, we can omit the relative pronoun if it is the object of the verb.

I've eaten the pasta (which) I made yesterday.

Defining relative clauses are not put in commas.


Non-defining relative clauses

Non-defining relative clauses give extra information about a noun. Use a comma before and after the relative clause.

That project, which I started years ago, still isn't finished.

Relative pronouns:
who/whom for people
which for things/group of people
where for places
whose for possessions belonging to people and things.

That can replace any pronoun except "whose" in defining relative clauses.

Use a relative pronoun after some of, all of, a few of, none of:

I have three sisters, none of whom are married.


Fixed prepositional phrases and relative clauses.

There are a number of fixed phrases which use preposition in a non-defining relative clause.
The company ran out of money, at which point I quit my job.
He may work late, in which case I'll get home first.
He watched the final, the result of which was never in doubt.

In informal sentenses, the preposition stays with the verb. In formal sentences we put the preposition before the relative pronoun.
He completed the book which he'd been working on (informal)
He completed the book on which he'd been working (formal)

Non-defining relative clauses are always set off from the rest of the sentence with commas, if it is removed from a sentence, we lose some detail, but the overall meaning of the sentence remains the same.

Relative clauses with who, which, that as subject pronoun can be replaced with a participle. This makes the sentence shorter and easier to understand. 

I spoke to the man who lives next door.
I spoke to the man living next door.