What kind of work permits are there in Europe?

For example, workers' and trade union legal rights in the United States are relatively restricted, compared to most European countries. However, the compartmentalization between different laws systems mean that illegal aliens, for example, may work in the same sectors as full citizens (although they most often work in difficult and tiring jobs which natives don't want). As a counter-example, if labor laws are more protective in France, due to social, historic and cultural differences, illegal aliens may not be legally contracted. Thus, they have a more difficult time finding jobs and often work in the underground economy. However, if they do manage to get residency or, better yet, be naturalized, than they will get better labor conditions than US immigrants.