The main focus of these notes is recent work on linear systems in which line arrangements play a role, including problems such as semi-effectivity, containment problems of symbolic powers of homogeneous ideals in their powers, bounded negativity, and a new perspective on the SHGH Conjecture. Along the way we will be concerned with asymptotic invariants such as Waldschmidt constants, resurgences and H-constants. Acknowledgements: My participation at the Spring, 2016 miniPAGES was partially supported by the grant 346300 for IMPAN from the Simons Foundation and the matching 2015-2019 Polish MNiSW fund. Some of the revisions to these notes were done at the Banach Center in Warsaw in the weeks after this material was presented at the workshop at the Pedagogical University in Krakow. I also thank J. Szpond for her helpful comments, and the referee for generously working though these notes and providing copious, helpful feedback.