There are exclamative sentences (or exclamative independent clauses):
What an incredible performance that was!
How lucky we are to have found this place!
Then there are exclamative clauses, which function like a noun clause:
He couldn’t imagine what a tough time they had.
I can’t tell you how proud they are of you.
Note that both independent and dependent clauses have been introduced by either what or how, but the latter lack exclamation sign (!).
This post goes further down the hierarchy and covers exclamative phrase.
An exclamative (or exclamatory) phrase is a phrase expressing strong emotions and opinions. They mostly take the form of noun phrase but sometimes that of adjective and prepositional phrase.
1. Exclamative noun phrase
Exclamative noun phrase comes in few varieties:
1.1. Regular noun phrase
These are regular noun phrases expressing approval or disapproval. Examples:
Approval
Lovely weather!
Lucky break!
Disapproval
Terrible news!
Awful situation!
They may express request, command, warning, and prohibition as well. Prohibition is like command, but it is preceded by No. Examples:
Request
A glass of water, please!
Two tickets, please!
The remote, if you wouldn’t mind!
Some help over here!
Command
Coffee! [Stop! won’t be an exclamative noun phrase. Stop is a verb, making Stop! an exclamative sentence.]
Tickets!
Notes!
The salt, right now!
Warning
Danger!
Fire!
Caution!
Police!
Prohibition
No entry!
No cell phones!
No photography!
No littering!
1.2. Noun phrase modified by relative clause
These exclamative noun phrases are formed by modifying noun phrases with relative clause, often with its relative pronoun omitted. They usually express disapproval. Examples:
The lies they told! [Exclamative noun phrase has been formed by modifying noun phrase The lies with relative clause they told. Relative pronoun that has been omitted.]
The mess they left behind!
The trouble they caused!
The effort he put into the project! [This doesn’t show disapproval though.]
1.3. Compound noun phrase
These exclamative noun phrases are compound structures formed by combining two noun phrases with and, one of which is commonly a pronoun (third example). They too express disapproval, though of a higher degree. Examples:
Mike and his constant complaining!
John and his never-ending excuses!
You and your late-night gaming!
Anna and her endless selfies!
2. Exclamative adjective phrase
Adjective phrases too can be exclamative. They express approval or disapproval. Examples:
Approval
Fascinating!
Absolutely fantastic!
Incredibly beautiful!
Disapproval
Quite annoying!
Extremely frustrating!
3. Exclamative prepositional phrase
Prepositional phrases starting with of all too can be exclamative. They express strong disapproval. Examples:
Of all the things to forget!
Of all the ridiculous ideas!
Of all the foolish mistakes!
Of all the thoughtless comments!
How exclamative phrases are used?
Exclamative phrases are sentence fragments, finding use mostly in speech. But they can be used in informal writing for variation and effect. Examples:
After the party, I was shocked to see what was left. Empty bottles were strewn everywhere, and used tissue papers covered the floor. I didn’t expect them to be so careless. The mess they left behind! It’s going to take hours to clean up.
Every time we meet, he has a new story. Last week, it was about a flat tire, and this week, it was about a family emergency. I’m so tired of hearing why he couldn’t make it. John and his never-ending excuses! It’s becoming impossible to rely on him.
