Permits based on work or studies

Residence permits under asylum legislation make up only approximately 1% of all residence permits for foreigners in Denmark. The vast majority are granted residence because they have found a job or have been accepted into higher education. There are also programs for au pairs, religious ministers and much more. Others are granted residence because of family ties, and as an EU citizen you have the right to settle down if you wish. All these cases are processed by SIRI (the Danish Agency for International Recruitment and Integration), but you can find information about them on the Danish Immigration Service's website nyidanmark.dk, also in English.
 
Although there is a big difference between applying for protection as a refugee and permission to live here as a student or worker, there is still some overlap. A rejected asylum seeker can in some cases be granted residence under EU rules if he marries a Danish citizen or has a child who is a Danish citizen. A refugee whose asylum protection is withdrawn can in some cases switch to a work permit. And a person who came here to study may end up getting asylum.
 
There are typically a couple of major obstacles when rejected asylum seekers try to obtain residence for other reasons. One is that a valid passport is required, and the application must usually be submitted from the home country, also for family reunification. Work and study permits generally require quite high qualifications – and proof of them. 
 
A residence permit as an employee or student can be very easily lost again and costs a lot of money. If you do not meet the conditions exactly, it will be withdrawn without mercy. 
 
As a student, you must first be admitted to a course of study, and you must pay for it yourself if you have not received a scholarship, e.g. under Erasmus. You are not entitled to housing or benefits (although you can get SU in some cases), and you must work a certain number of hours per year. After completing your education, you have a deadline to find a job, and that may give you a new option to stay. 
 
As a worker, there are two main paths: either you can get a residence permit based on your qualifications (the positive lists) and apply for a job after arrival, or you can get a contract with a company in Denmark in advance and get a residence permit for that reason (the pay limit scheme, fast track, researcher, etc.)
 
In general, asylum gives more rights, and it takes more to lose the residence permit again. A residence permit under EU rules, on the other hand, is a shortcut to permanent residence – you get it after 5 years without having to meet any other requirements than the original condition.

Read more:
Udlændingestyrelsen / nyidanmark.dk (full English version)
SIRI / siri.dk (very limited English version)
Study in Denmark / studyindenmark.dk (only in English)