Anyone who meets the criteria and requirements set by the European countries can work in Europe. Most European states have their programs, through which they tend to lure foreign professionals and fill job shortages in different fields in the country.

The Schengen work visa does not exist. You can get a Schengen visa for other purposes, as tourism, visiting family and friends, business, medical purposes etc. However, you cannot get a Schengen visa to work in Europe. You are not permitted to work while holding a Schengen visa for other purposes, as well.