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.