Although the pairing mechanism of the Fe-based superconductors (FeSCs) has not yet been settled with a consensus, as to the pairing symmetry and the superconducting (SC) gap function, the abundant majority of experiments are supporting for the spin-singlet sign-changing s-wave SC gaps on multibands (s^±-wave state). This multiband s^±-wave state is a very unique gap state per se and displays numerous unexpected novel SC properties such as a strong reduction of the coherence peak, non-trivial

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... urity effects, nodal-gap-like nuclear magnetic resonance (NMR) signals, various Volovik effects in the specific heat (SH) and thermal conductivity, and anomalous scaling behaviors with the SH jump and the condensation energy vs. T_c, etc. In particular, many of these non-trivial SC properties can be easily mistaken as evidence for a nodal gap state such as a d-wave gap. In this review, we provide detailed explanations of theoretical principles for the various non-trivial SC properties of the s^±-wave pairing state, and then critically compare the theoretical predictions with the experiments of the FeSCs. This will provide a pedagogical overview of how much we can coherently understand the wide range of different experiments of the FeSCs within the s^±-wave gap model.