Abstract: Recently, isomeric states are discovered for the first time in ¹⁰¹In, ^123,125Ag, and ²¹⁸Pa. The nuclear shell model is used to explain the underlying physics in these and related isomers in In, Ag isotopes, and the N\!=\!127 isotones. The observed excitation energies of the 1/2^- isomeric states in odd-A In isotopes, ^101-109In, are rather similar among five isotopes, which can be explained by introducing the strong neutron configuration mixing between the 0g_7/2 and 1d_5/2 orbitals. In addition, from the 9/2^+ ground state to the 1/2^- isomeric state in these odd-A In isotopes, a proton moves from the 1p_1/2 orbital to the 0g_9/2 orbital, which may induce the change on the single particle energies of the neutron 0g_7/2 and 1d_5/2 orbitals. Such configuration dependent shell evolution in one nucleus is called the type II shell evolution. Similar to In isotopes, the isomeric states in ^123,125Ag are found to be the 1/2^- states, which correspond to a proton hole in 1p_1/2 orbital. But 1/2^- states are ground states in ^115,117Ag, which indicates an inversion of the proton 1p_1/2 and 0g_9/2 orbitals around N\!=\!72. The shell-model analysis shows that the tensor force is the key reason of the inversion of the two orbitals. \rm A~1^- ground state and a high spin isomeric state are observed previously along the odd-odd N\!=\!127 isotones, ²¹⁰Bi, ²¹²At, ²¹⁴Fr, and ²¹⁶Ac. However, the ground state and the newly discovered isomeric state of ²¹⁸Pa are suggested to be 8^- and 1^-, respectively, based on the properties of \alpha decay and the shell-model calculations. The evolution of the ground states and isomeric states along the odd-odd N\!=\!127 isotones are caused by the transition of the proton-neutron interaction from particle-particle type to hole-particle type and the proton configuration mixing. In general, the nuclear shell model gives nice descriptions on these newly discovered isomeric states in nuclei around the doubly magic nuclei ¹⁰⁰Sn, ¹³²Sn, and ²⁰⁸Pb. The isomeric states in nuclei around doubly magic nuclei, so called the shell-model isomers, are of high importance in the nuclear structure study, because they often provide the first spectroscopic properties in the extreme neutron-rich and neutron-deficient nuclei in the medium and heavy mass region and include a plenty of information in physics, such as the proton-neutron interaction and its role in shell evolution.