The rules concerning Social Security claiming strategies are abundantly complex, especially if you're divorced. However, it's important to do your own research before you file for benefits for two important reasons: Social Security is more important to your retirement plan than you may suspect, and you cannot rely on Social Security employees to give you all of the options that are available to you. Nothing against the representatives of the Social Security Administration; they are professional and generally know their stuff, but they are there to answer your questions, and not necessarily there to advise you on all of your possible options.
First the basics: if your marriage lasted at least 10 years, you are still unmarried, you are age 62 or older and your ex-spouse is entitled to Social Security benefits, then you should qualify to receive benefits based on your ex-spouses record (regardless of whether they remarried or not).
Your benefits as a divorced spouse will be equal to 1/2 of your ex-spouses full retirement benefit. Assuming you begin taking benefits at your full retirement age (they will be reduced if you start collecting before then), it doesn't matter if your ex-spouse is currently receiving benefits or not. It only matters that they are eligible for benefits.
Here's where it gets interesting: by default, if you qualify for retirement benefits based on your own record, Social Security will compare your benefits to what you will receive as an ex-spouse, and you'll get the higher of the two benefits (it's a bit more complicated but it works out this way in the end). This may or may not be the best strategy for you.
If you were born before January 2, 1954, then your options are greatly expanded. If you qualify, you can choose to file for your divorced spousal benefits only, while letting the benefits based on your own record grow (deferred Social Security benefits grow at 8% per year after you've reached your full retirement age). Then, at age 70 (or anytime before), you can switch from receiving divorced spousal benefits to collecting benefits under your own record. Assuming of course, the deferred benefits under your own record are higher. Under this strategy, divorced spousal benefits are essentially "bonuses" and allow you to delay your own Social Security benefits, when you otherwise may not have been able to.
If your ex-spouse is deceased, then you should qualify for 100% of their full retirement benefit (instead of 50%). Social Security refers to this as a "surviving divorced spouse". You can start this benefit earlier than divorced spousal benefits, as soon as age 60. And if you were born before January 2, 1954, then the same claiming strategy described above applies. Except instead of getting 50% of your ex-spouses benefits, you should qualify for 100% while you wait to switch to your own benefits.
When using either strategy described above, it is critical that you only apply for one benefit when filing. Many filers inadvertently file for multiple benefits and in doing so limit their choices in the future.
For more information I'd suggest reading the Social Security Administration's "What Every Woman Should Know" report.