The TCV tokamak offers outstanding variability of the plasma shape. Using x-ray tomography, the shape of the inner flux surfaces of a poloidal cross section of the plasma can be reconstructed, including fast variations due to MHD activity. Both the hardware and the software of the 200 channel system developed for TCV are described. A new 'dynamical' calibration takes actual plasma parameters into account to determine the spectrum-dependent detector efficiency, resulting in an enhanced quality of reconstructions. Tomographic inversions are obtained using a variety of methods such as maximum entropy, linear regularization and a newly developed method based on the Fisher information. The merits of the different algorithms, which have been implemented as MATLAB functions, are compared. Inversion results are analysed with the help of singular-value decomposition, allowing, for example, identification of MHD modes without using any a priori information on the poloidal mode structure. Recent results on the dependence of sawtooth activity on the plasma triangularity are presented to demonstrate the performance of the soft x-ray tomography system.