Software fault prediction is an important activity in the testing phase of the software development life cycle and involves various statistical and machine learning techniques. These techniques are useful for making accurate predictions to improve software quality. Researchers have used different techniques on different datasets to build fault prediction in software projects, but these techniques vary and are not generalised. As a result, it creates challenges that make it difficult to choose a suitable technique for software fault prediction in a particular context or project. This mapping study focuses on research published from 1997 to 2020 involving fault prediction techniques, intending to determine a classification of fault prediction techniques based on problem types that researchers need to solve. This study conducted a systematic mapping study to structure and categorise the research evidence that has been published in fault prediction. A total of 82 papers are mapped to a classification scheme. This study identified research gaps and specific issues for practitioners, including the need to classify fault prediction techniques according to problem types and to provide a systematic way to identify suitable techniques for fault prediction models.