You can track a spouse. I am not talking about all the fancy tracking devices that police departments use either. Those are not usually available to the general public anyway. Those little contraptions are kept for the agency, although you might be able to find some things like this available at an electronics store. They might not be as effective as the ones the governments use, but they might actually work. Of course, you might have to worry about where you are going to place the tracking device.
You should not need a private detective to track a spouse either. This was the method that was widely used in the recent past. Private detectives became the way to find out what your spouse was doing. Unfortunately, modern advances this might not be as effective as it once was. Some of them will use of the advance to gather background information on people, but it does not help that much when you are tailing someone. They will still need to be really good at this skill to get the job done.
You can use modern technology to work to your advantage when you want to track a spouse now. There are programs that you can put on cell phones and other electronic devices that can give you a GPS location. Of course, this is only works if they have the device with them. If they leave it at home it will not work at all. It might be better to get a "bug" that you could stash in a shoe or something. Something that they would not leave the house without. Then again, not too many people actually leave home without their cell phones anymore.
Sometimes the programs that offer GPS do not allow you to just get on and track a spouse any time you want. What they do is give you the location at specific intervals through the day. So you might know where they where when the last one was recorded, but you might not be able to get a current location on them at that particular moment in time. These are nice because it is a program and not a "bug" that they might actually notice on the phone.
Of course, this is not the only way to track a stranger, but unless you are really good at blending in, or want to hire someone to physically track them; it may be the only option you have. You might try to get a friend of yours to help tail them, but that might put both of you in an awkward situation later. There are probably tons of other devices that you can get at an electronics store as well. I know you can get things like voice recorders as well as other "spy" equipment. It all depends on how implied you want to get with knowing where they are, and how much you are willing to spend for the knowledge. Private eyes are not cheap, and some of the other electronic equipment can get pretty expensive as well.