The development of handed asymmetry requires a special mechanism for consistently specifying a difference between left and right sides. This is to be distinguished from both random asymmetry, and from those left/right differences that are mirror symmetrical. We propose a model for the development of handedness in bilateral animals, comprising three components. (i) A process termed conversion, in which a molecular handedness is converted into handedness at the cellular level. A specific model for this process is put forward, based on cell polarity and transport of cellular constituents by a handed molecule. (ii) A mechanism for random generation of asymmetry, which could involve a reaction-diffusion process, so that the concentration of a molecule is higher on one side than the other. The handedness generated by conversion could consistently bias this mechanism to one side. (iii) A tissue-specific interpretation process which responds to the difference between the two sides, and results in the development of different structures on the left and right. There could be direct genetic control of the direction of handedness in this model, most probably through the conversion process. Experimental evidence for the model is considered, particularly the iv mutation in the mouse, which appears to result in loss-of-function in biasing, and so asymmetry is random. The model can explain the abnormal development of handedness observed in bisected embryos of some mammalian, amphibian and sub-vertebrate species. Spiral asymmetry, as seen in spiral cleavage and in ciliates, involves only conversion of molecular asymmetry to the cellular and multicellular level, with no separate interpretation step.