Abstract: The solar spectroscopic observation data provide importance source for the solar physics and the space weather research. The Extreme Ultraviolet (EUV) is the best optical band for observing the solar activities such as the flares and the coronal holes. The EUV imaging telescope and the slit spectrometer are the most important payloads onboard the solar observation satellites. The conventional solar EUV telescopes are capable of imaging the whole solar disk but without the spectral information. A slit spectrometer can obtain a high-resolution spectral image, but it takes too long time scanning an active area, which makes it difficult to catch the dynamics of the highly transient solar activities. These limitations make it very difficult to conduct the high-resolution observation of the solar activities and to study its mechanism. This paper introduces three different types of slitless spectrometer originated from 1970’s. The currently emerged multi-stage diffractive spectral imaging is detailed as a new type of solar EUV slitless imaging technique, which may serve as a reference for China’s space solar observation missions.