In this paper, the reader embarks on the first part of the review of school effectiveness research. The aim of the review is to offer a clearer picture on whether, which, and how much teacher and school variables impact student achievement, as there is currently no wider and accepted consensus on this matter, in spite of the wealth of various school effectiveness studies. An introduction is followed by a section on fragmented research paradigms. Four subsequent sections describe and critique findings from these paradigms, namely from student background, input-output, effective-schools, and instructional effectiveness studies. The paper concludes with the section on synthesis of findings, which implicate student background variables as the most important for student achievement, followed by instruction and teacher-related variables (in very poor developing countries, input-output factors are also relevant for student success). Subsequent paper will showcase more recent school effectiveness studies that use appropriate methodology and conceptual framework for identification of the most important school effectiveness factors.