  The combination of theory and simulation is necessary in the investigation of
properties of complex systems where each method alone cannot do the task
properly. Theory needs simulation to test ideas and to check approximations.
Simulation needs theory for modeling and for understanding results coming out
from computers. In this review, we give recent examples to illustrate this
necessary combination in a few domains of interest such as frustrated spin
systems, surface magnetism, spin transport and melting. Frustrated spin systems
have been intensively studied for more than 30 years. Surface effects in
magnetic materials have been widely investigated also in the last three
decades. These fields are closely related to each other and their spectacular
development is due to numerous applications. We confine ourselves to
theoretical developments and numerical simulations on these subjects with
emphasis on spectacular effects occurring at frontiers of different phases.
