1 Introduction

2 Examples

3 The Gyárfás-Sumner Conjecture

4 Variants of Gyárfás-Sumner: Rainbow Subgraphs

5 Variants of Gyárfás-Sumner: Orientations

6 Holes

7 Subdivisions

8 Graphs with Geometric Representations

9 Connections: The Erdős-Hajnal Conjecture

10 Gyárfás’ Complementation Conjecture

11 Operations on χ-bounded Ideals

12 Open Problems