'Tapering' is a feature for Curve objects in Blender.

Next to the "BevOb" button you now have a "TaperOb" button to give a name of a curve object which defines the width of extrusion of the 'Bevel Object' along the curve. The 'Taper Object' curve typically is horizontal, where the height denotes the scale of the width.

Important rules:

• Only the first curve in a TaperObj is evaluated
• The first width is left, last width is right
• Negative widths are possible too, but rendering can cause artifacts
• It scales the width of normal extrusions based on evaluating the taper curve, which means sharp corners in taper curve won't be easily visible 

That latter limitation could be improved by extrusing based on the exact points in the taper curve; which is for the todo list.