A growing need exists for efficient and accurate methods for detecting defects in semiconductor materials and devices. These defects can have a detrimental impact on the efficiency of the manufacturing process, because they cause critical failures and wafer-yield limitations. As nodes and patterns get smaller, even high-resolution imaging techniques such as Scanning Electron Microscopy (SEM) produce noisy images due to operating close to sensitivity levels and due to varying physical properties of different underlayers or resist materials. This inherent noise is one of the main challenges for defect inspection. One promising approach is the use of machine learning algorithms, which can be trained to accurately classify and locate defects in semiconductor samples. Recently, convolutional neural networks have proved to be particularly useful in this regard. This systematic review provides a comprehensive overview of the state of automated semiconductor defect inspection on SEM images, including the most recent innovations and developments. 38 publications were selected on this topic, indexed in IEEE Xplore and SPIE databases. For each of these, the application, methodology, dataset, results, limitations and future work were summarized. A comprehensive overview and analysis of their methods is provided. Finally, promising avenues for future work in the field of SEM-based defect inspection are suggested.