Experimental and theoretical studies of Ising superconductivity are considered. This new field of superconductivity starts with unusual properties of layered molybdenum disulfide (MoS₂) with unusually high upper critical magnetic field B_c2, 6 times exceeding the paramagnetic Pauli limit. This results from the crystal lattice properties of the two-dimensional monolayers, induced spin–orbital Ising and Rashba interactions. Specific crystal structure results in a possible coexistence of a singlet and triplet pairing, as well as appearance of the topological phases. Some variants of the Majorana fermion formations at the end of a long wire at the Ising superconductor surface are discussed.