  Interacting dipole ($p$) bosons along with scalar ($s$) bosons, based on the
ideas drawn from the interacting boson model of atomic nuclei, led to the
development of the vibron model based on $U(4)$ spectrum generating algebra for
diatomic molecules. The $U(4) \supset SO(4) \supset SO(3)$ algebra generates
rotation-vibration spectra. Extending this to two coupled $SO(4)$ algebras and
three $SO(4)$ algebras describe triatomic and four-atomic molecules
respectively. Similarly, appropriately coupled $U(2) \supset SO(2)$ algebras
will describe the stretching vibrations, with proper point group symmetries, in
polyatomic molecules. In addition, coupled $U(3)$ algebras describe coupled
benders. The Lie algebraic approach to molecular spectroscopy is briefly
described along with a list giving future directions and presented in three
appendices results for: (i) $U(3)$ algebra for bending vibrations and coupled
benders; (ii) symmetry mixing Hamiltonians generating regular spectra; (iii)
partition functions for diatomic and triatomic molecules.
