Who/that for persons

Which/that for things

The man who/that has the nice red car is our neighbour

Are you sure this is the house which/that my father wants to buy?

A defining relative clause gives important information and is therefore (deshalb) necessary for the sense of the whole sentence.
No commas are used to separate a defining relative clause from the rest of the sentence.

When the relative pronoun is the object of the relative clause, it is often left out (omitted):

Defining relative clause

Object

Here is the girl

that/who

you always wanted to meet.

Here is the girl

-

you always wanted to meet.

This is the house

that/which

I bought last year.

This is the house

-

I bought last year.

Relative clauses without a relative pronoun are called contact clauses.

!!! The relative pronoun cannot be left out if it is the subject of the relative clause:

Subject

Did you see the man

who

has just come into the room?

Who/whom for persons

Which for things

For persons, who is used when the relative pronoun is the subject, and whom is used when it is the object or when a preposition is used.

For things, which is used - never that in a non-defining relative clause. 

My friend, who was a football star in America,finally decided to move to Germany.

London Bridge, which is really busy with traffic, is the most famous bridge in London.

My uncle, whom I have never met, has a house in England.

She showed us some fantastic photos of Ayres Rock, which she visited on her last day.

The Millers, withwhom we went on holiday last year, are very nice people.

We climbed up the Post Office Tower, from which we had a wonderful view of London.

A non-defining relative clause gives additional / extra information. If it were left out, the rest of the sentence would still make sense. 

Commas are used to separate a non-defining relative clause from the rest of the sentence.

In a defining relative clause the preposition usually comes after the verb. Often the relative pronoun is left out completely (contact clause). 

In contact clauses the preposition always comes after the verb.

This is my uncle who I stayed with last year.

that I stayed with last year.
with whom I stayed last year.
I stayed with last year.

(contact clause)

I still remember the party that I went to last week.
which I went to last week.

to which I went last week.
I went to last week.
(contact clause) 

Relative clauses can also be introduced with 'whose'. It can refer to both persons and things. 'Whose' can be used in defining and non-defining relative clauses.

We met a man whose sister had emigrated to America (defining relative clause).

I called my brother whose bike had been stolen (defining relative clause).

The Millers, whose daughter is in Germany this year, decided to
invite us round for dinner (non-defining relative clause).

'Which' (in German 'was') can also be used to refer to a whole sentence. This kind of relative clause gives a comment on the whole of the sentence it refers to.

Relative clauses of this type are always non-defining.

Our new house is in one of the many suburbs of London, which can be an advantage but also a disadvantage.
(..., was ein Vorteil, aber auch ein Nachteil sein kann)