The concept of Research Integrity and research ethics are linked to the scientific research process and its communication. Presenting the results objectively is essential. It turns out that few scientists use manipulation of results and consequently other types of misconduct such as data Fabrication, Falsification, and Plagiarism (FFP). In this article, we show the definitions of these and different aspects of behavior that should be avoided, which affect principles of research reliability. We present, through a brief literature review, the concept of Research Integrity, FFP, and its relations with Publish or Perish. Editorial disputes are linked to the power that scientists have to remain in the field of research, governed by clear rules to increase their intellectual capital. We discussed that scientists tend to want their papers published in journals with better impact and well-evaluated, seeking prominence in the publishing sector. We have seen that both scientists and journals can have sequelae and problems in the face of the Publish or Perish movement, which can call into question the quality of the editorial process, peer review, and the journal itself.