A double-sided cutting insert with a plurality of indexable convex cutting edges can have a top face and a bottom face, at least three convex cutting edges on each face connected by at least three nose corners, at least three peripheral side surfaces extending from each face toward a virtual middle plane; and a common lateral seating surface on each peripheral side surface. Each convex cutting edge can have at least a curved cutting edge region, and can further have a primary substantially straight cutting edge region intermediate the curved cutting edge region and the nose corner. Each peripheral side surface can further have a primary planar facet associated with the primary substantially straight cutting edge, and each face may also be single-handed in same direction. Additionally, in various embodiments, the top and bottom faces of the cutting insert may be formed such that they are twisted or rotated with respect to each other. Further, additional cutting edges, edge regions, and/or surfaces may be included in a cutting insert in various embodiments. In such embodiments, the cutting insert or inserts may provide a powerful ramping function during milling operations.