Two-dimensional van der Waals heterostructures utilizing thin hexagonal boron nitride (h-BN) as a tunneling insulator have been proven as an interesting experimental platform for investigating electronics properties of low-dimensional systems. Here, we present electron tunneling spectroscopy measurements on various two-dimensional electronic systems comprised of graphene, h-BN, and transition metal dichalcogenides. With much improved tunnel junction stability of thin h-BN insulator, we are able to probe the electronic structures of two-dimensional systems such as Landau levels in graphene, an energy gap in bilayer graphene, secondary minibands formed in graphene superlattice structures, and the energy gap induced from the superconductivity in NbSe2 single crystals. With much improved signal-to-noise ratio, such novel tunneling features are monitored as varying charge density, tunneling bias voltage and an external magnetic field. We will present current understanding of the observed phenomena and discuss future research directions with a planar tunnel junction.