The majority of data collected and obtained from various sources over a patient's lifetime can be assumed to comprise pertinent information for delivering the best possible treatment. Medical data, such as radiographic and histopathology images, electrocardiograms, and medical records, all guide a physician's diagnostic approach. Nevertheless, most machine learning techniques in the healthcare field emphasize data analysis from a single modality, which is insufficiently reliable. This is especially evident in radiology, which has long been an essential topic of machine learning in healthcare because of its high data density, availability, and interpretation capability. In the future, computer-assisted diagnostic systems must be intelligent to process a variety of data simultaneously, similar to how doctors examine various resources while diagnosing patients. By extracting novel characteristics from diverse medical data sources, advanced identification techniques known as multimodal learning may be applied, enabling algorithms to analyze data from various sources and eliminating the need to train each modality. This approach enhances the flexibility of algorithms by incorporating diverse data. A growing quantity of current research has focused on the exploration of extracting data from multiple sources and constructing precise multimodal machine/deep learning models for medical examinations. A comprehensive analysis and synthesis of recent publications focusing on multimodal machine learning in detecting diseases is provided. Potential future research directions are also identified. This review presents an overview of multimodal machine learning (MMML) in radiology, a field at the cutting edge of integrating artificial intelligence into medical imaging. As radiological practices continue to evolve, the combination of various imaging and non-imaging data modalities is gaining increasing significance. This paper analyzes current methodologies, applications, and trends in MMML while outlining challenges and predicting upcoming research directions. Beginning with an overview of the different data modalities involved in radiology, namely, imaging, text, and structured medical data, this review explains the processes of modality fusion, representation learning, and modality translation, showing how they boost diagnosis efficacy and improve patient care. Additionally, this review discusses key datasets that have been instrumental in advancing MMML research. This review may help clinicians and researchers comprehend the spatial distribution of the field, outline the current level of advancement, and identify areas of research that need to be explored regarding MMML in radiology.