The transport phenomena of zero-gap conductors are one of the central subjects in condensed matter physics. α-(BEDT-TTF)₂I₃ [BEDT-TTF = bis(ethylenedithio)-tetrathiafulvalene] is a typical zero-gap conductor consisting of two-dimensional multiple two-dimensional layers. Under high pressures of above 1.5 GPa, it undergoes a phase transition to a zero-gap state, in which it exhibits unusual transport phenomena. This paper reviews the recent progress in clarifying the physics of α-(BEDT-TTF)₂I₃. In particular, the effect of a magnetic field on the behavior of electrons is investigated. On the basis of the interlayer magnetoresistance, evidence of the Landau level with the index N= 0 was obtained. The collaboration of experiments and theory has opened a new field of exploring the interlayer electron transport in two-dimensional layered zero-gap conductors. Furthermore, these phenomena have been observed by NMR and specific heat measurements in contrast to the case of graphene. The paper also reviews some recent topics including the role of multiple molecules in Dirac electrons, and the discovery of the quantum Hall effect.