Role of an adjective (they refer to a noun/pronoun in the main clause). Compare: I’d like to buy a large

That is especially common after quantifiers like all, every(thing), some(thing), any(thing), no(thing), none, little, few, much, only and after superlatives:
Is this all that’s left? (more natural than … all which is left)

I hope the little that I’ve done has been useful.

The only thing that matters is to find our way home.

It’s the best film that’s ever been made about madness.

Have you got anything that belongs to me?
Note that what cannot be used in these cases:

All that you say is certainly true. (NOT All what you say…)
2 types of relative clause:

• 
  DEFINING: They identify or classify a noun/pronoun.
  

They are necessary for the sense of the sentence.

They don’t have commas.

I’d like to meet a man who would make my dreams come true.

In this kind of clause we can omit the relative pronoun if it is not the subject of the relative clause:

He is the man (who/that) I met on holiday. (‘I’ is the subject)

I like the jeans (which/that) you bought yesterday. (‘you’ is the subject)

• 
  NON-DEFINING: They add extra information.
  

They are not necessary to the sense of the sentence.

They have commas.

The phone, which had been quiet all evening, suddenly rang.
We cannot omit the relative pronoun.

We cannot use that.

Another type of relative clause:
The relative pronoun which can be used to refer to the whole of the main clause, not just the subject/object:
He was very quiet, which is unusual for him.

He arrived at nine, which was when he was expected.

In this kind of sentence, which means and this/and that…

Note that what cannot be used in these clauses.

Prepositional relative clauses:
The preposition can go before the relative pronoun or at the end of a relative clause:
It’s a mystery for which there is no explanation. (more formal)

It’s a mystery which there is no explanation for. (less formal)

!!! After a preposition, we use which (not that) for things and whom (not who) for people.
Is this the place which/that we used to eat in? (informal)

Is this the place in which we used to eat? (formal)

Prepositional phrases are often used in non-defining relative clauses (very often in fixed expressions).
It might rain, in which case we will have to go home.

I waited for him until seven, at which point I gave up.

Pharaoh Tutankhamun’s tomb was opened in 1922, since when many strange things have happened.

There was a scandal, as a result of which all the ministers resigned.

The sunsets here are beautiful, which is why many artists come to paint them.

Shakespeare died in 1616, by which time he had written dozens of plays and poems.

Some of whom, none of which etc
In non-defining clauses, qualifying determiners (e.g. some, any, none, all, both, several, enough, many, few) can be used with of whom, of which and of whose.
They picked up five boat-loads of refugees, some of whom had been at sea for several months.

We’ve tested three hundred types of boots, none of which is completely waterproof.

Compare:
We’ve tested three hundred types of boots, but none of them is completely waterproof.

We’ve tested three hundred types of boots. None of them, however, is completely waterproof.

This structure is also possible with other expressions of quantity, with superlatives, with first, second, etc, and with last.

a number of whom, three of which, half of which, the majority of whom, the youngest of whom

Replacing relative clauses
We can often reduce a relative clause by omitting the relative pronoun and the auxiliary verb:
The man who was living next door… (active meaning → present participle used )

The wall, which was built during Roman times, still stands. (passive meaning → past participle used)

We can sometimes replace a relative clause with a to-infinitive:
He was the first person to reach the North Pole. (=who reached)

There’s no one here to speak to. (=who I can speak to)

Sue is the best person to ask. (that you can ask)