  Transformer, a deep neural network architecture, has long dominated the field
of natural language processing and beyond. Nevertheless, the recent
introduction of Mamba challenges its supremacy, sparks considerable interest
among researchers, and gives rise to a series of Mamba-based models that have
exhibited notable potential. This survey paper orchestrates a comprehensive
discussion, diving into essential research dimensions, covering: (i) the
functioning of the Mamba mechanism and its foundation on the principles of
structured state space models; (ii) the proposed improvements and the
integration of Mamba with various networks, exploring its potential as a
substitute for Transformers; (iii) the combination of Transformers and Mamba to
compensate for each other's shortcomings. We have also made efforts to
interpret Mamba and Transformer in the framework of kernel functions, allowing
for a comparison of their mathematical nature within a unified context. Our
paper encompasses the vast majority of improvements related to Mamba to date.
