Morphogen gradients provide embryonic tissues with positional information by inducing target genes at different concentration thresholds and thus at different positions. The Bicoid morphogen gradient in Drosophila melanogaster embryos has recently been analysed quantitatively, yet how it forms remains a matter of controversy. Several biophysical models that rely on production, diffusion and degradation have been formulated to account for the observed dynamics of the Bicoid gradient, but no one model can account for all its characteristics. Here, we discuss how existing data on this gradient fit the various proposed models and what aspects of gradient formation these models fail to explain. We suggest that knowing a few additional parameters, such as the lifetime of Bicoid, would help to identify and develop better models of Bicoid gradient formation.