This paper presents a review of models of the current transport in different kind of heterojunctions (HJs) and their characteristics. In order to effectively deduce the dominant electron transport for the HJs based on ZnO or Zn_1−xMg_xO layers grown on Si substrate by MBE a comparison is performed – which type of the HJ exhibits better electrical properties. The current–voltage characteristics for the studied HJs were measured within 280–300 K. The transport properties of the HJs are explained in terms of Anderson model with reference to aforementioned current transport models. It is found, that the mechanisms of current transport for all of the studied HJs are similar. At a low forward voltage bias the tunneling current dominates while at medium voltage bias (0.5–1 V) multitunneling capture-emission prevails with the electron trap located at 0.1–0.25 eV below the bottom of a ZnO (Zn_1−xMg_xO) conduction band. Beyond this voltage bias space charge limited current governs the current transport.