We have calculated the electron density distributions, electron densities at the bond critical point, and atomic charges in the period 2 and 3 fluorides and a number of their cations and anions. On the basis of this information and an analysis of X-F bond lengths, we have examined the factors that determine the lengths of these bonds. We have shown that all the molecules except NF3, Of(2), and F-2 have considerable ionic character. The bond lengths of the fluorides reach a minimum value at BF3 in period 2 and at SiF4 in period 3 when the product of the charges on the central atom and a fluorine reaches a maximum, consistent with a predominately ionic model for these fluorides. The length of a given A-F bond decreases with decreasing coordination number, and we show that it is determined primarily by packing considerations. This provides an alternative to the previously proposed back-bonding model explanation, for which our work provides no convincing evidence. There is also no evidence to support the Schomaker-Stevenson equation which has been widely used to correct A-F bond lengths calculated from the sum of the covalent radii of A and F for the difference in the electronegativities of A and F. We propose a new value for the covalent radius of fluorine and point out the limitations of its use.