Some migrate legally as permanent residents. Others come under arrangements that are nominally temporary, i.e. they are expected to work for a while and eventually return home. There is substantial illegal migration. Employers in rich countries can get people from poor countries to work for wages which are lower than those required by citizens but are higher than the workers can get in their home countries. Besides business employers, there are large numbers of private individuals employing foreign domestic workers.
Every rich country puts restrictions on the number of immigrants from poor countries.
Immigrants can become burdens on the welfare system, and if they bring their families, the families become burdens. The ratio of wages in many occupations between rich and poor countries is large enough to sustain a lot of overhead. Unless something surprising happens, China and India will sustain the low wage business for a very long time. The problem has several aspects. Communication Satellite communication may impose excessive control delays for fine work, especially if two satellites are involved.