4. SUMMARY

In spite of being known now for many decades, warps are still a puzzle. The observational situation and theoretical models to explain the data are still evolving. In this talk I have tried to summarize the situation as follows.

1. Warps are a very common phenomenon. However, in addition to the classic `grand-design' integral-sign warps, in many cases the warp is asymmetric or even one-sided. Models for warps should therefore not only address the symmetric, regular ones. Quite possibly there is a good analogy here to spiral structure, which also displays varying degrees of regularity.
2. Normal modes (equilibrium configurations of a tilted, warped disk precessing about the symmetry axis of a flattened halo) interact strongly with the dark halo. As a consequence they are easily and strongly damped, or, in special circumstances, excited.
3. Satellite tides are generally too weak to produce warps of the amplitudes observed. However the dark halo can under certain circumstances respond to the satellite in a way that significantly adds to the tidal perturbation on the disk. A useful diagnostic for satellite tides as explanation for a warp is the orientation of the warp with respect to the satellite orbit. In the case of the LMC / Galaxy system, this orientation appears to be different from predictions.
4. Accretion of material can generate warps through a continual change in the orientation of the halo symmetry plane, to which different parts of the disk respond on different timescales. Such models are yet to be investigated in full detail; in particular the question of whether the observed frequency of asymmetric warps can be reproduced by this kind of model may be a useful avenue to explore.