Use semicolons to separate independent clauses not joined by a conjunction:

The weather is gloomy; we are all very depressed. (This can also be expressed as two sentences.)

May be used between clauses in a long compound sentence, even when they are joined by a conjunction.

The university has won so many awards in these fields that students are on waiting lists for applications, begging for interviews, and trying to bribe the admissions officers for special consideration; but the admissions procedures are not changing as a result of this newfound fame.

To separate clauses linked with the following adverbs: then, however, thus, hence, indeed, accordingly, besides, and therefore:

The Nobel Prize winners are most pleased; indeed, they are planning a huge celebration.

The geologist discovered a new mineral; therefore, she is naming it after herself.

To separate items in a series that is long and cumbersome or that contains internal commas:

The students should take one course in math; three in languages; two chosen from political science, history, or art; and one senior capstone course.