The Author's Enemy - the Semicolon

Out of all the various punctuation marks I have ever encountered, memorized, or used the semicolon has hands down given me the most trouble. I constantly find myself running back to grammar and punctuation books. According to "The Writer's Handbook" 

Semicolons help you connect closely related ideas when a style mark stronger than a comma is needed. By using semicolons effectively, you can make your writing sound more sophisticated.

Sounds simple right? And yet this little daub of ink gives many authors loads of trouble. Employers know this. I once had an interview for a job that required strict writing skills and they went right for the jugular. 

"What are semicolons used for?"

I suppose that this weeds out the serious writers from the merely competent. It certainly threw me for a loop.  Really what makes this one so hard?