This paper charts the development of spectrally efficient forms of optical orthogonal frequency division multiplexing (OFDM) that are suited for intensity-modulated direct detection systems, such as wireless optical communications. The journey begins with systems using a DC-bias to ensure that no parts of the signal that modulates the optical source are negative in value, as negative optical intensity is unphysical. As the DC-part of the optical signal carries no information, it is wasteful in energy; thus asymmetrically clipped optical OFDM was developed, removing any negative-going peaks below the mean. Unfortunately, the clipping causes second-order distortion and intermodulation, so some subcarriers appear to be unusable, halving spectral efficiency; this is similar for unipolar and flipped optical OFDM. Thus, a considerable effort has been made to regain spectral efficiency, using layered techniques where the clipping distortion is mostly cancelled at the receiver, from a knowledge of one unpolluted layer, enabling one or more extra ‘layers/paths/depths’ to be received on the previously unusable subcarriers. Importantly, for a given optical power and high-order modulation, layered methods offer the best spectral efficiencies and need the lowest signal-to-noise ratios, especially if diversity combining is used. Thus, they could be important for high-bandwidth optical fibre systems. Efficient methods of generating all layers simultaneously, using fast Fourier transforms with their partial calculations extracted, are discussed, as are experimental demonstrations in both wireless and short-haul communications links. A musical analogy is also provided, which may point to how orchestral and rock music is deciphered in the brain.This article is part of the theme issue ‘Optical wireless communication’.