Computer tomography (CT) is a common medical imaging modality. Most of CT scans today are done in the helical mode with two-dimensional detector arrays. Image reconstruction from data provided by such scans is a complicated problem. On one hand, very good image quality is required. On the other hand, the algorithm has to be highly efficient. In this talk we present a reconstruction algorithm that combines these two features. Mathematically, image reconstruction in helical CT is a problem of integral geometry, which consists of recovering an unknown function f knowing its integrals along lines intersecting a helix. We will describe also a more general inversion formula, which recovers f knowing its integrals along lines intersecting a fairly arbitrary curve in R3. This formula is of interest in other versions of CT, most notably in C-arm scanning.