Optical OFDM was proposed for dispersion compensation in long-haul optical communications systems in 2006 in two forms, one using direct-detection and the other using coherent detection. Since then there has been extensive innovation towards developing intermediate forms of optical OFDM that are more suited to specific applications. This review paper presents our view on the developments in optical OFDM for long-haul optical transmission applications. It covers the basic elements of radio OFDM before concentrating on direct detection optical OFDM and its development, followed by coherent optical OFDM. All-optical OFDM is then considered, together with optical methods of generating and separating the OFDM subcarriers. The paper then discusses the critical issue of nonlinear degradation due to the Kerr effect in optical fibers and reviews recent innovations to mitigate the effects of fiber nonlinearity. Finally some future research directions are discussed.