The application of machine learning to radiological images is an increasingly active research area that is expected to grow in the next five to ten years. Recent advances in machine learning have the potential to recognize and classify complex patterns from different radiological imaging modalities such as x-rays, computed tomography, magnetic resonance imaging and positron emission tomography imaging. In many applications, machine learning based systems have shown comparable performance to human decision-making. The applications of machine learning are the key ingredients of future clinical decision making and monitoring systems. This review covers the fundamental concepts behind various machine learning techniques and their applications in several radiological imaging areas, such as medical image segmentation, brain function studies and neurological disease diagnosis, as well as computer-aided systems, image registration, and content-based image retrieval systems. Synchronistically, we will briefly discuss current challenges and future directions regarding the application of machine learning in radiological imaging. By giving insight on how take advantage of machine learning powered applications, we expect that clinicians can prevent and diagnose diseases more accurately and efficiently.