  We develop a tight-binding model description of semi-Dirac electronic
spectra, with highly anisotropic dispersion around point Fermi surfaces,
recently discovered in electronic structure calculations of VO$_2$/TiO$_2$
nano-heterostructures. We contrast their spectral properties with the well
known Dirac points on the honeycomb lattice relevant to graphene layers and the
spectra of bands touching each other in zero-gap semiconductors. We also
consider the lowest order dispersion around one of the semi-Dirac points and
calculate the resulting electronic energy levels in an external magnetic field.
We find that these systems support apparently similar electronic structures but
diverse low-energy physics.
