All shape memory binary alloys (SMBA) that exhibit not only perfect shape recovery but also partial shape recovery were reviewed and classified into three groups, B2, A2 and A1 type, according to the parent phases. There are the thirteen, six and eleven alloys belonging to B2, A2 and A1 type, respectively. In the group of B2 type SMBA the alloys are divided into two categories due to the combination of the elements. Over A1 and A2 type SMBA the atomic composition of one element is larger than the other so the larger one is called a major element. The major elements, Ti, U, Fe, and Cu, of A2 type SMBA do not belong to the group 5 and 6 in which the elements have a typical BCC (A2) crystal structure. In the A1 type SMBA there are four major elements, Mn, Fe, Co, and In and the SMBA except for In-based SMBA have ferromagnetic or antiferromagnetic natures. The shape memory effect (SME) for A1 (FCC) type SMBA might need the magnetic properties.