under · preposition /ˈʌn.dər/Full view
A1 below something, or below the surface of something
Dictionary examples:

He hid under the bed.

They were standing under a tree.

She was holding a file under her arm.

She pushed her bag under the table.

He could only keep his head under the water for a few seconds.

Learner example:

I like my bedroom, because there [is] a table under the window, [and] some pictures on the wall. (Skills for Life (Entry 1); A1; Arabic)

under (LESS THAN)
A2 less than a number, amount, or age
Dictionary examples:

All items cost/are under a pound.

You can buy the whole set of DVDs for just under £30.

The discount applies only to children under (the age of) ten.

Under-5s get in free.

If you get under 50%, you've failed the exam.

Learner example:

I saw an advertisement in front of my house: the coffee bar is looking for some waiters aged under 23 years old. (Preliminary English Test; B1; Italian)

B2 in a particular state or condition
Dictionary examples:

The President is under pressure to resign.

Under no circumstances should the festival become too specialized.

Learner example:

I am used to working under pressure. (First Certificate in English; B2; Polish)

under attack/control/investigation, etc.
B2 being affected by something at the present time
Dictionary examples:

The town is once again under attack.

The cause of the fire is still under investigation.

A new 16-screen cinema is under construction.

Several different plans are under discussion.

We are working hard to get the situation under control.

Learner example:

Everything was under control, the remote detonator had worked perfectly well. (First Certificate in English; B2; Spanish)

be under the impression
B2 to think or understand a particular stated thing
Dictionary examples:

I was under the impression (that) you didn't get on too well.

He was under the mistaken impression (that) you were married.

Learner example:

I am under the impression that people generally exercise a little, but if they eat the wrong food every day, it won't help. (First Certificate in English; B2; Danish)

under your breath
C2 If you say something under your breath, you say it very quietly so that other people cannot hear it.
Dictionary example:

He was muttering curses under his breath.

Learner example:

"We must have taken a wrong turn somewhere..." he kept muttering under his breath. (Certificate of Proficiency in English; C2; Spanish)

down under
C2 Australia, or in Australia
Dictionary example:

She was born in Scotland, but she's been living down under for 22 years.

Learner example:

Last year a good friend of mine and I went to Australia. After a couple of days of doing some sightseeing and sunbathing on bea[u]tiful sandy beaches, we decided that we need[ed] to get something more out of our stay down under. (Certificate of Proficiency in English; C2; Polish)

under your nose
C2 If something bad happens under your nose, it happens close to you but you do not notice it.
Dictionary example:

They were stealing money from under my nose.

Learner example:

You will be surprised that there was something right under your nose that you could not live without. (Certificate of Proficiency in English; C2; Korean)

be under way
C2 to be already happening
Dictionary example:

Building work is already under way.

Learner example:

Sociologists are well-aware of the fact and experiments are under way to counterbalance these disadvantages. (Certificate of Proficiency in English; C2; French)

be/feel under the weather
C2 to feel ill
Dictionary example:

I'm feeling a bit under the weather this morning.

Learner example:

Ann was a bit under the weather, [and] she felt quite lonely in her big flat. (Certificate of Proficiency in English; C2; Italian)

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