From BlenderWiki
Bevel Modifier
Mode: Any mode
Panel: Modifiers (Editing context, F9)
Description
The Bevel modifier adds the ability to bevel the edges of the mesh it is applied to, allowing control of how and where the bevel is applied to the mesh.
What is a Bevel?
The definition of a bevel, according to wikipedia.org, is:
 « A beveled edge refers to an edge of a structure that is not perpendicular (but instead often at 45 degrees) to the faces of the piece. The words bevel and chamfer overlap in usage; in general usage they are often interchanged, while in technical usage they may sometimes be differentiated… »
The picture (Unbeveled square) shows a square which has unbeveled edges as the angles between the corners of the square are 90° (perpendicular). The picture (Beveled square) shows a square which has beveled corners.
Although the two pictures above show 2D squares, the Blender Bevel modifier can work on both 2D and 3D meshes of almost any shape, not just squares and cubes…
The picture (Default bevel) shows a Blender 3D cube whith a bevel applied using just the default Bevel modifier settings.
Setting Bevel Weight
When certain bevel options (such as BevWeight in the Bevel modifier) are set, the mesh will need to have bevel weights assigned to it, otherwise the bevel will not be applied.
Bevel weights can be applied to selected edges of a mesh by:
 Switching to Edit mode.
 Selecting the edge or edges of the mesh that you wish to assign a bevel weight to.
 Pressing Ctrl⇧ ShiftE or going to menu entry Mesh » Edges » Adjust Bevel Weight.
 Then by moving the mouse around, or entering a value directly at the keyboard between 1.0 to +1.0, you should be able to change the default bevel weight. You will be able to see the current value of the bevel weight change at the bottom status area of the 3D Viewport.
 If the mesh already has a Bevel modifier with the BevWeight button enabled, as you alter the bevel weights, you should see the bevel amount changing in real time.
Options
The Bevel modifier panel is a reasonably uncluttered panel and, for the most part, intuitive. That said, here is a description of the settings contained within this panel:
 Width
 The Width numeric field controls the width/amount of the bevel applied to the base mesh. It can range from 0.0 (no bevel applied) to 0.5 (Blender Units). This value is in fact the “backing up” of the two new edges relatively to the original (beveled) one, along the two concerned faces.
 Only Vertices
 The Only Vertices button alters the way in which a bevel is applied to the mesh. When it is active, only the areas near vertices are beveled, the edges are left unbeveled.
 Limit Using:
 This section of the Bevel modifier is used to control where and when a bevel is applied to the underlying mesh. The first row of three buttons (mutually exclusive) controls the algorithm used, and might add some extra options.
 None
 This button will apply the Bevel modifier to the whole underlying mesh, without any way to prevent the bevel on some edges/vertices.
 Angle
 This button will only bevel edges where faces make sharp angles. When selected, it displays the Angle numeric field, used to set the angle above which an edge will be beveled (it is in fact the complementary angle, i.e.
180°(angle between faces)
). When the angle between meeting faces is less than the angle in the slider box, the bevel on those specific edges will not be applied. Similarly, when the angle between two edges is less than this limit, the vertex is not beveled.
 BevWeight
 This button will force the Bevel modifier to take into account any bevel weights that may or may not be assigned to the edges of the underlying mesh. When the BevWeight button is active, and at least some of the edges are bevel weighted, the Bevel modifier will bevel each edge according to its weight.
 When the BevelWeight button is active, three extra buttons appear underneath it, named Min, Average and Max. They control how the bevel weighted influences are calculated and assigned at places where two or more bevel weighted edges meet, that have different weights. Obviously when there are several bevel weighted edges which are directly linked/connected to each other, there needs to be a way to determine which particular bevel weight gets assigned at the point of contact between them (interpolation vertex point in the diagrams of the three cubes, below).
 Min
 When several bevel weighted edges with different weights meet, the interpolation/contact point between them will take the smaller of the bevel weights as the one for this point (see
Cube 1
to the right).  Average
 When several bevel weighted edges meet, the interpolation/contact point between them will take the average value of the bevel weights as the one for this point (see
Cube 2
to the right).  Max
 When several bevel weighted edges meet, the interpolation/contact point between them will use the larger of the bevel weights as the one for this point (see
Cube 3
to the right).
Note
Thanks to Xalt for making clear how the limit using BevWeight Min, Average and Max buttons affect underlying meshes.  Terrywallwork  28th June 2008.

See Also
 The old and deprecated Bevel tool.