Molecular beam epitaxy (MBE) of cubic group III-nitrides is a direct way to eliminate polarization effects which inherently limit the performance of optoelectronic devices containing quantum well or quantum dot active regions. In this contribution, the latest achievement in the MBE of phase-pure cubic GaN, AlN, and AlN/GaN quantum wells will be reviewed. The structural, optical, and electrical properties of state of the art cubic nitrides and AlGaN/GaN will be presented. We show that no polarization field exists in cubic nitrides and demonstrate intersubband absorption at 1.55 µm in cubic AlN/GaN superlattices. Comparing the experimental results with simulations based on an effective-mass model the GaN/AlN conduction-band offset is demonstrated to be higher than 1.2 eV. The best fit with the experimental data is achieved for a conduction-band offset of 1.4 eV. Further the progress toward the fabrication of cubic GaN/AlGaN superlattices for terahertz applications will be discussed and our first experiments on cubic AlN/GaN resonant tunneling devices will be reported.