In recent years, some of the promised potential of biomedical photoacoustic imaging has begun to be realised. It has been used to produce good, three-dimensional, images of blood vasculature in mice and other small animals, and in human skin in vivo, to depths of several mm, while maintaining a spatial resolution of <100 μm. Furthermore, photoacoustic imaging depends for contrast on the optical absorption distribution of the tissue under study, so, in the same way that the measurement of optical spectra has traditionally provided a means of determining the molecular constituents of an object, there is hope that multiwavelength photoacoustic imaging will provide a way to distinguish and quantify the component molecules of optically-scattering biological tissue (which may include exogeneous, targeted, chromophores). In simple situations with only a few significant absorbers and some prior knowledge of the geometry of the arrangement, this has been shown to be possible, but significant hurdles remain before the general problem can be solved. The general problem may be stated as follows: is it possible, in general, to take a set of photoacoustic images obtained at multiple optical wavelengths, and process them in a way that results in a set of quantitatively accurate images of the concentration distributions of the constituent chromophores of the imaged tissue? If such an 'inversion' procedure - not specific to any particular situation and free of restrictive suppositions - were designed, then photoacoustic imaging would offer the possibility of high resolution 'molecular' imaging of optically scattering tissue: a very powerful technique that would find uses in many areas of the life sciences and in clinical practice. This paper describes the principal challenges that must be overcome for such a general procedure to be successful.© (2009) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.