In this work, two advanced snapshot field-integral hyperspectral imaging spectrometers are presented. The first system is based on image mapping mirrors and achieves significantly increased datacube size and dynamic range compared to previous generations. This benefits from a novel design and fabrication method for making the large-format multifaceted mapping mirrors based on the two-photon grayscale lithography (2GL) mode from a commercial two-photon polymerization(2PP) printer. The new fabrication technique can accelerate the fabrication process, increase facet density, eliminate edge eating, and reduce shadowing effects. Additionally, images combining the IMS and dual inverted selective plane illumination microscope (diSPIM) are demonstrated for high spatial and spectral resolution 5D imaging (x,y,z,λ,t). The second system is a fiber-based snapshot hyperspectral imaging spectrometer which can work in both visible (490 nm-732 nm) and short-wave infrared (1090 nm - 1310 nm) wave ranges. A customized relay system with a high numerical aperture (NA) and large field of view (FOV) is designed, fabricated, and then implemented in the spectrometer to overcome the light collection efficiency problems in previous systems. The new relay system enables imaging with a fast frame rate and/or under low illumination conditions. The aims of this work are to advance the two hyperspectral imaging techniques to broaden their applications in biomedical imaging and remote sensing.