You can live a rich and satisfying life without ever using a semicolon... even if you are an academic.
When writing web content, avoid the semicolon. In theory, it breaks up a long sentence. But in practice, the semicolon clutters up the page instead of creating white space (unlike the full stop). So it frightens people. It also has a negative effect on people using Twitter.
However, the semicolon still has one useful function. In certain formal documents—for example, legal documents—the use of dot points may be forbidden. Luckily, a semicolon can differentiate among items in a complex list.
Terrible sentence... but correct use of semicolon
The plaintiff claimed that her ex-partner had removed from her office 32 pencils and 32 whiteboard markers; 4 boxes each of A4 manilla envelopes and regular white window envelopes; and a cubic metre of polystyrene packing chips stored in a clear plastic bag.