  While the propagation of tsunamis is well understood and well simulated by
numerical models, there are still a number of unanswered questions related to
the generation of tsunamis or the subsequent inundation. We review some of the
basic generation mechanisms as well as their simulation. In particular, we
present a simple and computationally inexpensive model that describes the
seabed displacement during an underwater earthquake. This model is based on the
finite fault solution for the slip distribution under some assumptions on the
kinematics of the rupturing process. We also consider an unusual source for
tsunami generation: the sinking of a cruise ship. Then we review some aspects
of tsunami run-up. In particular, we explain why the first wave of a tsunami is
sometimes less devastating than the subsequent waves. A resonance effect can
boost the waves that come later. We also look at a particular feature of the 11
March 2011 tsunami in Japan - the formation of macro-scale vortices - and show
that these macro-scale vortices can be captured by the nonlinear shallow water
equations.
