That's why you hear about some tech founders offering their side project to the company they work for before they continue with their venture. The company can decide to keep it or you can agree with the company that they don't want it and you can keep it.
In theory, they can sell you the rights to your own project if that's what they want to do. It's what you agreed to in your contract.
In short, take it very seriously. If you have a side project that you think can be a successful venture for you then get an ok from your employer to make sure they have no claim on it.
Companies can sue anywhere but the further you are from them the harder it is. Like anything, you can always take your chances that it's not worth their time to pursue. But it's much easier to just get a release of all claims on your project from them.