The interview follow-up is a courteous letter of acknowledgment. It is a good idea to write a follow-up thank you letter anytime a company has invested time with you. The letter should show the reader that you are thorough, courteous, efficient, and sincerely interested in the job. On the personal level, writing this letter allows you to wrap up your application for the job; it is your last chance to tie up all the loose ends neatly.
The follow-up letter required when you receive no response to an interview is the subtlest of the follow-up letters. It is normally used on two occasions reasons: either the company is painfully slow in making decisions, or you have other offers pending and you want to hurry the decision along.
If you have other offers, you must in all fairness contact the firms who have spent money and time on your interviews and visits to the firm before accepting another position. The main purpose of the letter is to request that a decision about your application be made.