Building roofing produced with asbestos-containing materials is a significant concern due to its detrimental health hazard implications. Efficiently locating asbestos roofing is essential to proactively mitigate and manage potential health risks from this legacy building material. Several studies utilised remote sensing imagery and machine learning-based image classification methods for mapping roofs with asbestos-containing materials. However, there has not yet been a critical review of classification methods conducted in order to provide coherent guidance on the use of different remote sensing images and classification processes. This paper critically reviews the latest works on mapping asbestos roofs to identify the challenges and discuss possible solutions for improving the mapping process. A peer review of studies addressing asbestos roof mapping published from 2012 to 2022 was conducted to synthesise and evaluate the input imagery types and classification methods. Then, the significant challenges in the mapping process were identified, and possible solutions were suggested to address the identified challenges. The results showed that hyperspectral imagery classification with traditional pixel-based classifiers caused large omission errors. Classifying very-high-resolution multispectral imagery by adopting object-based methods improved the accuracy results of ACM roof identification; however, non-optimal segmentation parameters, inadequate training data in supervised methods, and analyst subjectivity in rule-based classifications were reported as significant challenges. While only one study investigated convolutional neural networks for asbestos roof mapping, other applications of remote sensing demonstrated promising results using deep-learning-based models. This paper suggests further studies on utilising Mask R-CNN segmentation and 3D-CNN classification in the conventional approaches and developing end-to-end deep semantic classification models to map roofs with asbestos-containing materials.