  The modeling of complex systems such as ecological or socio-economic systems
can be very challenging. Although various modeling approaches exist, they are
generally not compatible and mutually consistent, and empirical data often do
not allow one to decide what model is the right one, the best one, or most
appropriate one. Moreover, as the recent financial and economic crisis shows,
relying on a single, idealized model can be very costly. This contribution
tries to shed new light on problems that arise when complex systems are
modeled. While the arguments can be transferred to many different systems, the
related scientific challenges are illustrated for social, economic, and traffic
systems. The contribution discusses issues that are sometimes overlooked and
tries to overcome some frequent misunderstandings and controversies of the
past. At the same time, it is highlighted how some long-standing scientific
puzzles may be solved by considering non-linear models of heterogeneous agents
with spatio-temporal interactions. As a result of the analysis, it is concluded
that a paradigm shift towards a pluralistic or possibilistic modeling approach,
which integrates multiple world views, is overdue. In this connection, it is
argued that it can be useful to combine many different approaches to obtain a
good picture of reality, even though they may be inconsistent. Finally, it is
identified what would be profitable areas of collaboration between the
socio-economic, natural, and engineering sciences.
