For the first year, you're tied to your employer. After that, you're free to change jobs, but only within your field of work.
You need to reapply for the work permit when you change jobs or every two years (max validity duration), which is quite painless. After 4 years you should get permanent residence, and no longer need any permits.. This is the process for most non-EU residents.
It's (for now, anyway) a fairly routine process. If you've been a legal, self-sufficient resident of Sweden for 4 years, you get permanent residency after a straightforward application.
There is some debate over adding a Swedish-language requirement, but there isn't currently one. That is one of the two difference with Denmark: if you're a non-EU immigrant to Denmark, you need to live there 5 years under the same conditions rather than 4, plus pass a middle-level Danish competency exam.
You need to reapply for the work permit when you change jobs or every two years (max validity duration), which is quite painless. After 4 years you should get permanent residence, and no longer need any permits.. This is the process for most non-EU residents.