Computed tomography perfusion (CTP) is a functional imaging that allows for providing capillary-level hemodynamics information of the desired tissue in clinics. In this paper, we aim to offer insight into CTP imaging which covers the basics and current state of CTP imaging, then summarize the technical applications in the CTP imaging as well as the future technological potential. At first, we focus on the fundamentals of CTP imaging including systematically summarized CTP image acquisition and hemodynamic parameter map estimation techniques. A short assessment is presented to outline the clinical applications with CTP imaging, and then a review of radiation dose effect of the CTP imaging on the different applications is presented. We present a categorized methodology review on known and potential solvable challenges of radiation dose reduction in CTP imaging. To evaluate the quality of CTP images, we list various standardized performance metrics. Moreover, we present a review on the determination of infarct and penumbra. Finally, we reveal the popularity and future trend of CTP imaging.