Recent advances in whole-genome studies provide increasingly strong evidence for a vital role of hybridisation in fortifying species and allowing them to adapt to new environments. To represent such complex evolutionary histories as a web of life rather than a simple bifurcating tree of life, phylogenetic (evolutionary) networks have become a popular tool. In comparison with trees, phylogenetic networks — which are graphs with underlying cycles — do not only represent speciation events but, additionally, allow for the representation of processes (e.g. hybridisation) in which distinct species recombine their genetic material and create a new species. In this talk, we investigate how tools from graph theory and theoretical computer science can be used to develop new algorithms that reconstruct a phylogenetic network from a collection of phylogenetic trees.