Triple grain junctions in polycrystals become important at the nanoscale, as the fraction of atoms in them reaches a considerable value. They have an associated line tension, as grain boundaries have a boundary tension. We discuss the definition of line tension and its effects on: a) the equilibrium angles at which three-dimensional (3D) grain boundaries meet; b) the kinetics of 3D grain growth, particularly the kinetic exponent in the power relation between average grain diameter and time, and the possible existence of a scaling regime in grain growth. We conclude that the triple junctions tend to slow down grain growth and predict "anomalous" effects when the line tension is negative.