The English verbs discussed below all relate a whole thing to its parts. There is some confusion of this set of verbs by native speakers of English,* and there is also some controversy, so the correct meanings and proper usage of these words are worth considering.

Comprise and consist of

These two verbs both indicate what parts belong to a whole. They are interchangeable.

Examples:
The whole comprises its parts.
The whole consists of its parts.

Both verbs specify a complete accounting or listing of the parts that make up the whole. If I say, for example, that my computer system comprises an iMac, a keyboard, an iSub sub-bass woofer and an external hard disk drive, it means that there are no other components in my system.

Constitute, compose and make up

These verbs all indicate what whole thing is constituted by a collection of parts. They are interchangeable in that meaning.

Examples:
The parts constitute the whole.
The parts compose the whole.
The parts make up the whole.

Similarly to 'comprise' and 'consist of', these verbs specify the complete set of parts. If I say that an iMac and a keyboard constitute my computer system, it means that my system has only those two parts.

include

This verb specifies the parts that belong to a whole. It has the same meaning as 'contain'. It differs from 'comprise' and 'consist of' in that it can specify either all or only some of the parts, although the latter meaning is perhaps most intended.

Examples:
My system includes an external hard drive and an internal optical drive. (But there are also other components.)
Her system includes three laptop computers connected by Ethernet. (And nothing else.)

The Confusion

The biggest problem is confusing the sense of 'comprise' with the sense of 'constitute' or 'compose', particularly when comprise is incorrectly used in the passive voice to mean constitute or consist of rather than the correct 'be composed of'.

Improper:
The legislative, judicial and executive branches comprise the US government. (Parts cannot comprise the whole.)
The US government is comprised of legislative, judicial and executive branches. (Making the verb 'comprise' passive does not change the relationship of parts to whole.)

Proper:
The legislative, judicial and executive branches constitute the US government.
The US government comprises (or consists of or is composed of) the legislative, judicial and executive branches.

The Controversy

The improper uses described above are being seen and heard increasingly often, and examples of misuse can be found in literature. The American Heritage Dictionary cites an example from Saul Bellow, "Put together the slaughterhouses, the steel mills, the freight yards ... that comprise the city". This trend in usage is reaching the point where it could be argued that the rule should be changed to fit the way people are actually using these terms. (See Language change or language corruption?.) One reason to resist such change, if it comes from lack of education or laziness, is that the change disrupts the original logic or clearness in distinction, thus making the language harder to learn and use consistently.

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*This is true for American English at least; I'm not sure if this is also true for speakers of other English dialects, although a number of readers have suggested that it is.