Technology is such that users of cell phones and even land lines can specify that their phone number not be visible to the recipient of the call. This feature is heavily used by telemarketers and newspaper reporters, as well as people who are on a limited calling plan and do not want to be called back except at certain times.
However, this feature can also be used by someone who wants to play a prank, or--more rarely--to deliver insults and threats. The telephone company as well as your local law enforcement agency has ways to find out who is making unwelcome phone calls to your line.
Make a note of the time and day when the first call comes in. Call the customer relations number of your service provider. If you are calling on a cell phone, it's usually a three-digit direct number from that phone.
Find out what is needed to trace a call. Usually, the phone company will require you to contact law enforcement, although some will agree to furnish phone numbers to the police if you establish a pattern. The phone company is not likely to trace a number after one annoying call.
Keep your log, writing down the date and time of each call, and what is said on each call. You are entitled to protection from harassing calls, even if they are just constant hang-ups or heavy breathing.
After a pattern is established, the law enforcement officer assigned to your case will take your log to the phone company and pursue the caller. In some cases, If the caller is varying phones, or calling from a public phone, there will be "trap" set. The trap will require you to keep the caller on the line and call the police on another line so they can work with the phone company to find the exact location of the caller.
Prosecute the case. This is an agreement you will have to make with the police before they will proceed. They will not commit police resources simply to satisfy your curiosity.
If you suspect you are being annoyed by kids, or are not threatened at all, it might work to simply discourage the caller by pretending you are tracing the call, or using a high-decibel whistle. If you know you are being called by a stalker, or a former spouse, boyfriend or girlfriend, you have protection under the law without having to establish a pattern. Discuss the matter with an attorney and get an injunction against this harassment.
Call the police right away if there are calls threatening your life or property. If you go forward with catching the caller, be sure to prosecute. Invasion of privacy should be stopped.