Factor and fractional graph theory are hot topics on modern mathematics. As a generalization, factor and fractional factor are widely used in many fields related to computer science. In this book, we study some topics on factor and fractional factors. Several bounds are given for the existence of factor and fractional factors avoiding some given graphs. In the first chapter, we list all the concepts and lemmas which we use in this book. In the second chapter, we give the binding number conditions for fractional (g, f, n’)-critical graphs and fractional (a, b, n’)-critical graphs. In the third chapter, we study the binding number conditions for fractional (g, f, n’)-critical deleted graphs and fractional (a, b, n’)-critical deleted graphs. In the fourth chapter, we research the conditions for a graph has a factor avoiding some given subgraphs. In the last chapter, we pose some open problem for our further study.