We investigate tunneling in metal-insulator-metal junctions employing few atomic layers of hexagonal boron nitride (hBN) as the insulating barrier. While the low-bias tunnel resistance increases nearly exponentially with barrier thickness, subtle features are seen in the current-voltage curves, indicating marked influence of the intrinsic defects present in the hBN insulator on the tunneling transport. In particular, single electron charging events are observed, which are more evident in thicker-barrier devices where direct tunneling is substantially low. Furthermore, we find that annealing the devices modifies the defect states and hence the tunneling signatures.Van der Waals heterostructures, where layered stacks of two dimensional materials are embedded in precisely desired patterns, have gained immense attention in recent times 1,2 . Such tailor-made structures of graphene, hexagonal boron nitride (hBN), metal dichalcogenides and other 2D materials offer exotic device geometries to explore new physics. Tunnel junctions with an atomically thin insulator barrier sandwiched between atomic layers of 2D materials form an interesting structure in this respect. In conventional two dimensional semiconductor double layer structures, tunneling has shown remarkable features, including resonant tunneling, Coulomb correlations at high magnetic fields and Landau-level spectroscopy 3-6 . In the regime of 2D layered materials, hBN with a band gap of âź 5.9 eV 7 is an ideal candidate for an insulating barrier 8 . Recent studies on heterostructures with single and bilayer graphene as electrodes and hBN as the insulator have shown interesting features, including a very strong negative differential resistance (NDR) 9-12 . In all of these transport studies hBN is assumed to be a benign element. However, from a materials perspective there have been extensive efforts to understand the underlying structure and defect mechanisms in thin layers of hBN, which can have important consequences on electrical transport 13-15 . Here we present detailed tunneling transport measurements on simple junctions consisting of metal or graphite electrodes separated by a thin hBN layer. Our results demonstrate that the hBN insulator can yield unexpected transport signatures suggestive of defect-mediated tunneling processes.In a conventional metal-insulator-metal (M-I-M) junction, the tunnel current-voltage characteristic (I-V ) is linear at low biases, with the tunneling resistance inversely proportional to sample area and exponentially dependent on the barrier thickness d. Our studies show that the I-V with hBN as the barrier is distinct from such a simple behavior in various respects. Thinner barrier devices show a finite linear tunnel current at low biases and a roughly exponential dependence of the low bias resistance with d, complying with standard quantum mechanical tunneling, in agreement with previous reports 9,12 . However, in relatively thicker barrier devices, h--BN