The article draws attention to the difficulties in functioning as a pupil and peer of children of other cultures (migrants) who have to find themselves in a new educational and social reality after coming to Poland. There will be special analysis made of migrant children (of other nationalities), who mainly face language competence deficits and, consequently, adaptation and educational problems. The educational system has to more often face the new challenges of teaching and bringing up multicultural students (belonging to different national, ethnic, linguistic, and religious). For them, Polish is usually a foreign language that significantly influences the quality of their social contacts and educational achievements. Language proficiency is therefore crucial for school success and integration. One of these challenges is to accurately and reliably identify the needs of students with multiple difficulties at different levels of education to organize effective psychological and pedagogical assistance. The article draws attention to the key elements of the diagnostic process which include: a diagnostician, a child, a parent (subjects in the research relationship), and research methods and tools (subjects). The issue of limitations of the process of diagnosing specific learning and social difficulties becomes particularly important here, as well as identification of barriers resulting from the search for effective assistance solutions.