The report is an overview of the insight into the phenomenology when using wall penetrating radar, gained in the project "Local Urban Battlefield Surveillance" and other FOI work, as well as from some international theoretical and experimental studies. Reflection, transmission and attenuation of the radar wave are treated in the report for various wall types, from simple homogeneous, plane sheets, to inhomogeneous stratified walls, hollow walls, reinforced concrete walls and/or rough walls displaying diffuse scattering. The focus is on frequencies about 10 GHz. The attenuation varies between wide limits, from low for indoor plasterboard walls to high for concrete walls, as manifested by FOI measurements and calculations; the significance of moisture content is established through systematic measurements. The possibility to use the so-called Brewster effect to maximize the penetration into a wall, with oblique incidence and vertical polarization is pointed out. By detailed field calculations performed in the project, the influence of the wall on the pointing accuracy has been determined for a monopulse antenna system, being held against the wall. Thereby the significant wall return in the backward direction has been noticed and propositions made to alleviate the effect. With wall penetrating radar in general, one may be forced to compensate for the influence of the wall, if reasonable system performance is to be obtained, e.g. with image generation of the region behind a wall. International studies of how this is to be done are described. Field calculations have been performed in the project of inhomogeneities in the form of reinforced concrete walls. They show that reflection and transmission vary strongly with the type and dimensions of the bars. In the report an account is given of work on modeling and of analytical calculation methods for the study of the influence of wall roughness, and also measurements of metalized rough building materials. Experimental and theoretical studies of hollow concrete show a severely distorted wave field close to the wall, with a strong deterioration of direction estimates of e.g. monopulse antennas. If possible, the sensors should be placed further away from the wall. Having passed through the first wall further into a building the wave propagation quickly becomes intractable, with a host of possibilities for further interactions with stationary and moving objects, where discrimination of targets is attempted. For specific statements, elaborate computer calculations are required for the case in question. The inhomogeneities and the multipath propagation are however positive elements for focusing of e.g. an antenna array by means of time reversion (wave front reversion) , whose application for image generation is more difficult to predict. In the project a case has been simulated containing a scanning 10 GHz radar, monitoring movements of a human behind a wall, in a room. The target returns are smeared out both in Doppler and in range, which diminishes the possibility to study so-called micro-Doppler, caused by e.g. arm and leg movements. Finally, the report gives a sketch of current ideas of how an advanced mapping ofthe interior of buildings should be accomplished. A methodology is described that includes model-based reasoning in an iterative, closed-loop scheme, where a model of a building is constructed, layer by layer. Work along these lines is in progress in the US VisiBuilding project.