The study of molecules characterized by translational ultracold temperatures (T < 1mK) is an exciting and rapidly developing frontier in Atomic, Molecular, and Optical Physics. Of particular interest are heteronuclear molecules with a significant dipole moment. The particular case of KRb will be discussed in detail: (a) KRb formation from ultracold atoms K and Rb by photoassociation[PA] [or magnetoassociation]; (b) the detection of the highly excited internal states of the KRb molecule produced by PA; (c) the transfer of molecules from these highly excited internal states to the lowest rovibronic level, symbolized X(0,0), where inelastic rovibronic collisions are energetically forbidden. The ability to efficiently produce KRb molecules in the X(0,0) level offers considerable opportunities for studies of ultracold collisions, new quantum phases of matter, quantum information applications, and the corresponding effects of electromagnetic fields.