An X-ray is the well-known probe to examine structure of materials, including our own bodies. The X-ray beam, especially at the wavelength of nanometers, has also become significant to directly investigate electronic states of a sample. Such an X-ray is called a soft X-ray and polarization dependence of the light-matter interaction further unveils the microscopic properties, such as orbitals or spins of electrons. Generation of high brilliant beams of the polarized X-ray has linked to development of our experimental science, and it has been made by radiation from relativistic electrons at the synchrotron radiation facilities over the world. Recently, we constructed a new polarization-controlled X-ray source, the segmented cross undulator, at SPring-8, the largest synchrotron radiation facility in the world. The operation is based on interference of X-ray beams, which is sharply contrast to the conventional method of regulating electron trajectory by the mechanical control of magnets. The paradigm shift opened the measurement innovations and allowed us to design new experimental approaches to capture signals that have been hidden in materials. The present review describes the novel X-ray source with the principle of operation and the technical details of optimization. Examples of the frontier spectroscopies that use unique optical properties of the source are introduced, followed by the future prospects for next generation synchrotron radiation facilities.