The magnetic phase diagram of Ising spin chains packed into the frustrated triangular lattice is discussed. A structure of a low-temperature phase depends strongly on interactions between the next-to-nearest-neighbor chains because they lift the degeneracy of the triangular AFM Ising model. That is why, a variety of low-temperature phases is observed in CsCoCl3, Ca3Co2O6, and Sr5Rh4O12. On the contrary, the high-temperature phase (honeycomb AFM structure) is unique. The frustrated Ising chain systems demonstrate an unusual and very slow magnetization dynamics. A model of the magnetization dynamics similar to the Glauber theory is developed.