Dynamic computed tomography (CT) imaging aims at reconstructing image sequences where the dynamic nature of the living human body is of primary interest. The main applications concerned are image-guided interventional procedures, functional studies and cardiac imaging. The introduction of ultra-fast rotating gantries along with multi-row detectors and in near future area detectors allows huge progress toward the imaging of moving organs with low-contrast resolution. This paper gives an overview of the different concepts used in dynamic CT. A new reconstruction algorithm based on a voxel-specific dynamic evolution compensation is also presented. It provides four-dimensional image sequences with accurate spatio-temporal information, where each frame is reconstructed using a long-scan acquisition mode on several half-turns. In the same time, this technique permits to reduce the dose delivered per rotation while keeping the same signal to noise ratio for every frame using an adaptive motion-compensated temporal averaging. Results are illustrated on simulated data.