  The world of network science is fascinating and filled with complex phenomena
that we aspire to understand. One of them is the dynamics of spreading
processes over complex networked structures. Building the knowledge-base in the
field where we can face more than one spreading process propagating over a
network that has more than one layer is a challenging task, as the complexity
comes both from the environment in which the spread happens and from
characteristics and interplay of spreads' propagation. As this
cross-disciplinary field bringing together computer science, network science,
biology and physics has rapidly grown over the last decade, there is a need to
comprehensively review the current state-of-the-art and offer to the research
community a roadmap that helps to organise the future research in this area.
Thus, this survey is a first attempt to present the current landscape of the
multi-processes spread over multilayer networks and to suggest the potential
ways forward.
