A cutting insert for milling operations, such as, face milling, slot milling, plunge milling, and ramping operations. The cutting insert exhibits a combination of favorable cutting edge strength, and unique cutting edge geometry, thus, allowing milling operations at relatively high feed rates. The cutting insert includes at least four cutting edges, wherein at least one of the cutting edges is a convex cutting edge. Certain embodiments of square cutting inserts will have four convex cutting edges which may be connected by nose corners. The convex cutting edge may comprise at least one of a circular arc, a portion of an ellipse, a portion of a parabola, a multi-segment spline curve, a straight line, or combinations of these. Wherein the convex cutting edge comprises a circular arc, the circular arc may have a radius greater than or equal to two times a radius of the largest circle that may be inscribed on the top surface.