Crooks no longer need much of your personal information to steal your identity.  By combining some real and fake credentials, thieves can open accounts in your name, obtain mortgages, and create one big mess that you won’t benefit from, but will definitely have to clean up.  Monitoring your credit reports is always a good idea.  But it won’t necessarily spot synthetic identity theft. 
So in addition to ordering your credit reports at least once a year, some experts also recommend using identity monitoring services.  They scour public records to find other potential pieces of your background (or the background of someone claiming to be you).  You can find many of them by simply putting “background checks” into an internet search engine.  These reports may generate information on consumers with names that are similar to yours, but it may be a way for you to spot activity that someone could mistake as yours.