Why is my smoke detector beeping?

The smoke detector in my apartment has been beeping intermittently (~every 30 seconds) for the last 20 minutes or so. It is not going off in alarm mode, because I know what that sounds like. Just short beeps.

I do not see or smell any signs of smoke (although I do have a terrible sense of smell), and I’ve opened all the windows. What could be going on?

Replace the battery.

This is typically the indication that the battery is getting low, and that you need to replace the battery.
(should be explained in the owner’s manual)

Your battery needs replacing.

Ah thanks. I don’t have an owner’s manual because I’m not the owner, and my landlord is always a pain to deal with since they barely speak English. I’ll try to tell them about it.

If you can safely reach the smoke detector, it’s a simple enough job to do yourself. Look at the cover and see if there are opening instructions, maybe the word “Pull” with an arrow or something. If you don’t see any anywhere, try pulling the cover down by pulling the edge downwards. It should swing down on a hinge. Some open with a push-and-twist like a childproof cap–try both directions. In any case, once you get the thing open the battery, a standard 9V alkaline, usually just snaps out. The new one goes right in the same way. Close the cover again, and you’re set. Press the Test button to be sure you have the battery in correctly.

Just a quick addition to Q.E.D.'s excellent instructions – press and HOLD the test button. All the smoke alarms I’ve dealt with required holding down the button for one or two seconds before they’d emit their ever-so-pleasant squeal.

Addendum - When you have to change the clocks to account for daylight saving or standard time, make it a habit to replace the batteries in your alarms. Yeah, changing the batteries every six months may appear as overkill, but when it comes to fire and smoke, it’s a small inconvenience in time and cost.

Check it out when you replace the battery, it’s likely to be the only thing in your house that contains a trans-uranic element.

If a new battery doesn’t help, try moving it to a warmer location as a test. I purchased several models before I found one that didn’t do this when my basement grew cold in winter.

Jurisdictions vary, but the battery replacement is probably not his responsibilty, but yours. And if a fire breaks out and it’s discovered that you intentionally removed the battery and didn’t replace it, you might be liable for all damages.
You probably signed a separate paper to that effect when you moved in. It would have also told you to push the Test button once a month. In this state it’s in the state guidebook for landlords and tenants.