This thesis deals with problems concerning the local properties of graphs with large chromatic number in hereditary classes of graphs.
We construct intersection graphs of axis-aligned boxes and of lines in R3 that have arbitrarily large girth and chromatic number. We also prove that the maximum chromatic number of a circle graph with clique number at most ω is equal to Θ(ωlogω). Lastly, extending the χ-boundedness of circle graphs, we prove a conjecture of Geelen that every proper vertex-minor-closed class of graphs is χ-bounded