1 Introduction

2 Preliminaries

3 The FGF on 𝑅𝑑

4 The FGF on a domain

5 Projections of the FGF

6 Fractional Brownian motion and the FGF

7 Restricting FGFs

8 Regularity of FGF(D)

9 The eigenfunction FGF

10 FGF local sets

11 Spherical decomposition

12 The discrete fractional Gaussian field

13 Open questions