While problems on colored point sets have been receiving substantial attention, colored line arrangements have not been much explored. However, despite the duality between the two type of problems, some questions are only natural or appealing in the second scenario.

In this talk we mention some previous research on the topic, and describe several recent results that we have proposed and coauthored, coming from [1,2,3].

1. Coloring and Guarding Arrangements. P. Bose, J. Cardinal, S. Collette, F. Hurtado, S. Langerman, M. Korman, P. Taslakian. Presented at 28th European Workshop on Computational Geometry, Assisi, Italy, March 2012.

2. Balanced Partitions of 3-colored Geometric Sets in the Plane. S. Bereg, F. Hurtado, M. Kano, M. Korman, D. Lara, C. Seara, R. Silveira, J. Urrutia, K. Verbeek. Presented at 29th European Workshop on Computational Geometry, Braunschweig, Germany, March 2013.

3. Cell-Paths in Mono- and Bichromatic Line Arrangements in the Plane. O. Aichholzer, J. Cardinal, T. Hackl, F. Hurtado, M. Korman, A. Pilz, R. Silveira, R. Uehara, B. Vogtenhuber, E.Welzl. Proc. 25th Canadian Conference on Computational Geometry, Waterloo, Canada, August 2013.