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The identification of charge stripes in La{sub 2{minus}x{minus}y}Nd{sub y}Sr{sub x}CuO{sub 4} (Nd-214) has reenergized research on the original high transition temperature {Tc} superconductor, La{sub 2{minus}x}Ba{sub x}CuO{sub 4} (Ba-214), and related compounds. Early in the study of Ba-214, a low temperature phase transition was associated with changes in electrical properties. An apparent suppression of {Tc} near Ba x=0.125, was initially associated with a first order low temperature phase transformation. However, it was later shown that only very near Ba x=0.125 was {Tc} reduced markedly, and that the relationship between crystal structure and {Tc} is more complicated. This review well describe the low temperature crystal structures and microstructures, as well as the superconducting properties as determined from low field (1-100G) dc magnetometer measurements for Ba-214, Nd-214, and La{sub 2{minus}x}Sr{sub x}CuO{sub 4} (Sr-214). The authors will also describe some work in the related La{sub 2{minus}x}Ca{sub x}CuO{sub 4} (Ca-214). A basic knowledge of the interactions among superconductivity and low temperature phases will allow one to better understand the significance of the underlying charge stripe phases.