Discrete Geometry is a broad area with many interesting topics. This presentation covers a subarea of discrete geometry called combinatorial convexity, centered around the colorful Caratheodory theorem by Imre Barany. We will cover some of my personal favorites among variations and extensions of Barany's theorem. If time permits, I will introduce some introductory texts, weblogs, journals or lecture notes where we can learn some more about this area.