We show that, because of the inevitable twist and lattice mismatch in heterobilayers of transition metal dichalcogenides, interlayer excitons have six-fold degenerate light cones anomalously located at finite velocities on the parabolic energy dispersion. The photon emissions at each light cone are elliptically polarized, with major axis locked to the direction of exciton velocity, and helicity specified by the valley indices of the electron and the hole. These finite-velocity light cones allow unprecedented possibilities to optically inject valley polarization and valley current, and the observation of both direct and inverse valley Hall effects, by exciting interlayer excitons. Our findings suggest potential excitonic circuits with valley functionalities, and unique opportunities to study exciton dynamics and condensation phenomena in semiconducting 2D heterostructures.PACS numbers: 74.78. Fk, 78.67.Pt, 72.25.Fe Monolayers of group-VIB transition metal dichalcogenides (TMDs) have recently emerged as a new class of direct-gap semiconductors in the two-dimensional (2D) limit [1][2][3][4][5]. These hexagonal 2D crystals have exotic properties associated with the valley degeneracy of the band edges, including the valley Hall effect [6,7], the valley magnetic moment [8][9][10][11], and the valley optical selection rules [6,[12][13][14][15][16], leading to rich possibilities for valley-based device applications. The visible range bandgap further makes these 2D semiconductors ideal platforms for optoelectronics. Due to the strong Coulomb interaction, the optical response is dominated by excitons, the hydrogen-like bound state of an electron-hole pair. The demonstrated electrostatic tunability and optical controllability of valley configurations of excitons in monolayer TMDs have implied new optoelectronic device concepts not possible in other material systems [13][14][15][16][17].Stacking different TMDs monolayers to form van der Waals heterostructures opens up a new realm to extend their already extraordinary properties [18]. MoX 2 /WX 2 (X=Se, S) heterobilayers have been realized [19][20][21][22][23][24][25], which feature a type-II band alignment with the conduction (valence) band edges located in MoX 2 (WX 2 ) layer. Exciton then has the lowest energy in an interlayer configuration (i.e. electron and hole in different layers), from which luminescence is observed [19][20][21]. Due to the spatially indirect nature, interlayer excitons in MoSe 2 /WSe 2 heterobilayers have shown long lifetime exceeding nanosecond, repulsive interaction, and electrostatically tunable resonance [19], all of which are highly desirable for the realization of excitonic circuits and condensation [26][27][28][29]. An unprecedented aspect of this interlayer exciton system is that the heterobilayers in general have incommensurate structures due to lattice mismatch and twist in the stacking which, together with the valley physics inherited from the monolayers, bring in radically new properties.Here we discover anomalous light coupling prope...