In the early seventies several papers appeared considering the effect of the ICM on galaxies in clusters, e.g. ram pressure stripping (Gunn and Gott 1972), evaporation (Cowie and Songaila 1977) and turbulent viscosity and evaporation (Nulsen 1982). Not much work was done though to connect theory with observations. The first paper that specifically looks at observational characteristics is the paper by Stevens, Acreman and Ponman (1999). This paper focusses on the impact of the ICM on an elliptical galaxy with a hot ISM and calculates the observational signatures of this in the hot ICM, predicting bow-shocks, wakes and tails. Some, but still precious few, examples of structures that could be interpreted like this exist in the X-ray literature (Stevens et al. 1999). Observationally, there is much more evidence for the impact of the ICM on the cool ISM of disk galaxies. From a view point of galaxy evolution this is also the more important question. In clusters star formation rates are known to evolve rapidly between intermediate redshifts and the local universe (Poggianti et al 1999, Balogh et al 1999). A mechanism is required to bring star formation almost completely to a halt and a major issue is whether ram pressure stripping could do this to disk galaxies. The original analytical estimates of Gunn and Gott (1972) predict that gas gets stripped from a galaxy up to a stripping radius within which the restoring force from the disk exceeds the ram pressure. The first numerical simulations (Abadi, Moore and Bower (1999)) using a 3 dimensional SPH/N-body simulation to study ram pressure stripping of gas from spiral galaxies orbiting in clusters confirm that gas in disk galaxies gets stripped up to the stripping radius estimated by Gunn and Gott (1972). At small radii the potential provided by the bulge component contributes considerably. They estimate that a galaxy passing through the center of Coma would have its gaseous disk truncated to 4 kpc, losing about 80% of its gas. However the process is in general not efficient enough to account for the rapid and widespread truncation of star formation observed in cluster galaxies. Quilis, Moore and Bower (2000) use a finite difference code to achieve higher resolution in order to be able to include complex turbulent and viscous stripping at the interface of cold and hot gaseous components as well as the formation of bow shocks in the ICM ahead of the galaxy. From only a few selected runs on galaxies with holes in the central gas distribution they reverse the conclusion of Abadi et al. (1999) and state that ICM - ISM interaction could explain the morphology of S0 galaxies and the rapid truncation of star formation implied by spectroscopic observations. The main difference with the Abadi et al. result is the use of a complex multi phase structure of the ISM. They show that the presence of holes and bubbles in the diffuse H I can greatly enhance the stripping efficiency. As the ICM streams through the holes in the ISM it ablates the edges and prevents stripped gas from falling back. Schulz and Struck (2001) in a comprehensive study using SPH, an adaptive mesh HYDRA code, and including radiative cooling, confirm that low column density gas is promptly removed from the disk. They also find that the onset of the ICM wind has a profound effect on the gas in the disk, that does not get stripped. The remnant disk is compressed and slightly displaced relative to the halo center. This can trigger gravitational instability, angular momentum gets transported outward and the disk compresses further forming a ring. This makes the inner disk resistant to further stripping, but presumably susceptible to global starbursts. These various simulations appear to more or less agree on the effects of the ISM. All of the above work modelled the ICM as a constant wind. Vollmer et al. (2001) took a different approach. Using an N-body/sticky-particle code they simulate galaxies in radial orbits through the gravitational potential of the Virgo cluster. The galaxies thus experience a time variable ram pressure and maximal damage to their gaseous disks only becomes apparent well after closest approach to the Virgo Cluster center. Thus if we see galaxies with truncated H I disks or distorted velocity fields they are likely to be on their way out from the center. They also find that a considerable part of the stripped total gas mass remains bound to the galaxy and falls back onto the galactic disk after the stripping event, possibly causing a central starburst. The results of Schulz and Struck (2001) and Vollmer et al (2001) are the first to produce simultaneously stripping in the outer parts and a mechanism to enhance star formation in the inner parts. This may help use up any remaining gas in the central regions and it could possibly do some secular bulge building. There is observational evidence for stripped H I disks with enhanced central H I surface densities (Cayatte et al. 1994) and there are several lines of evidence that the most recent episode of star formation in cluster galaxies occurred in the central parts (e.g. Rose et al. 2001).