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We present the concept, some of the approaches used, and the capabilities of the technique referred to as GPS tomography. It is used for retrieval of the 3-dimensional distribution of the refractivity due to atmospheric water vapor. We discuss the presently used methods for retrieval of the primary observable in the GPS tomography, the slant path delay, as well as their shortcomings. Comparisons of GPS slant delays to independent data from a microwave radiometer are included. From a tomographic point of view we concentrate on the capabilities to retrieve the vertical structure of the wet refractivity. For this purpose we present and apply two methods for tomographic inversion. Both are based on the Kalman filtering technique, where the expected statistical behavior of the refractivity is utilized. The difference between the two is in the way the covariance matrix of the Kalman filter is constructed. We base our study on simulated and real data from the ground network of 8 GPS receivers operating in Göteborg, Sweden. The results demonstrate that at present the limitations of the GPS tomographic technique are errors in the retrieved wet slant delays and their poor geometric distribution.