If it wishes to keep tabs on you, there are a number of ways for the FBI to to do so. One of the most known and popular ways is the car tracker. You've seen it in movies and TV shows, and probably read about its use in the news. You would think that the tech behind such a device would be some next-level shit, but it's not.
After looking at iFixit's Teardown of an FBI tracking device, we see that it's basically built with run-of-the-mill technology. There are some interesting tidbits, like how it runs on as little as .125 MB of SRAM and 1 MB of flash memory. Or that the battery pack has double the capacity of an iPad 2 and can last up to 20 years.