We review the recent deep learning reconstruction algorithms for spectral snapshot compressive imaging (SCI), which used a single shot measurement to capture the three-dimensional (3D, x, y, λ) spectral image. Recent years, deep learning has been the dominant algorithm to conduct reconstruction due to high speed and accuracy. Various frameworks such as end-to-end neural networks, deep unfolding, plug-and-play networks have been developed. Furthermore, the untrained neural networks have also been used. In this paper, we review diverse deep learning methods for spectral SCI. In addition to the aforementioned frameworks, different backbones and network structures including the most recent Transformers are reviewed. Simulation and real data results are presented to compare these methods.