Many important maps in algebraic combinatorics (the RSK bijection, the Schutzenberger involution, etc.) can be described by piecewise-linear formulas. These formulas can then be ``de-tropicalized,'' or ``lifted,'' to subtraction-free rational functions on an algebraic variety, and certain properties of the combinatorial maps become more transparent in the algebro-geometric setting. I will illustrate how this works in the case of the promotion map on semistandard tableaux of rectangular shape. I will also indicate how promotion can be viewed as the combinatorial manifestation of a symmetry coming from representation theory, and how its geometric lift fits into Berenstein and Kazhdan's theory of geometric crystals.