In my talk I would like to present an introduction to complex conic-line arrangements in the projective plane. We will start with an intriguing construction of the Chilean configuration of conics (or the Hesse arrangement of conics) which has some unexpected properties. This is going to be our Letimotif example. Then I will discuss some positivity and negativity properties related to conic-line arrangements, mostly in the context of Harbourne indices and (time permitting) Seshadri constants. At the end of my talk I would like to put conic-line arrangements into the perspective of log-surface.
Based on a joint works: with Tomasz Szemberg arXiv:2002.01760 and Marek Janasz (preprint soon on arXiv)