This is a brief account of the earlier history of single-particle cryo-EM of biological molecules lacking internal symmetry, which goes back to the mid-seventies. The emphasis of this review is on the mathematical concepts and computational approaches. It is written as the field experiences a turning point in the wake of the introduction of digital cameras capable of single electron counting, and near-atomic resolution can be reached even for smaller molecules.Key words: 3D reconstruction, image processing, ribosome, molecular structureThe spectacular, fast-paced advances in single-particle cryogenic electron microscopy (cryo-EM) in the past 3 years, following the introduction of novel direct detection device (DDD) cameras with superior signal-to-noise ratio and resolution [1,2], are currently the subject of many commentaries and news and views articles conveying the general excitement of the structural biology community and the scientific community at large. As someone who has been in the field since the early days, I would like to contribute by a recollection of how the field developed.Single-particle EM, as a novel approach to structural biology, required a heretical concept going against the grain of wisdom which held that quantitative structure determination by 3D reconstruction from EM projections [3] is not feasible unless molecules are arranged in crystalline order. These ordered structures include those with helical symmetry, as in DeRosier and Klug's reconstruction of a bacteriophage tail [3], arranged in a two-dimensional crystal [4,5], or with high symmetry as in viruses [6]. Viruses, although classifiable as single particles, contain structural information in a highly redundant form. For instance, the projection of a virus with icosahedral symmetry contains 60 projections of its asymmetric unit. Not only is the spatial arrangement of these units fixed and recoverable from the Fourier transform, but the signal is also retrieved with an instant bonus of nearly 8-fold reduction in the power of noise. Crowther and coworkers, in developing the common lines approach for recovering the structure of an icosahedral virus from its projection, did state that 'there is in principle no reason why the method should not be extended to systems with lower symmetry' [6], but it was not apparent how this could be practically accomplished for objects lacking symmetry altogether.At the time, the idea of single-particle averaging of entirely asymmetric molecules [7] therefore created some excitement: If such, [i.e. asymmetric single-particle] methods were to be perfected, then, in the words of one scientist, the sky would be the limit [8]. Thus, Robinson's Research News article started with an appreciation of Unwin and Henderson's seminal work, the 3D reconstruction of bacteriorhodopsin