We present a spectroscopic overview of the C-H center dot center dot center dot Y (Y = hydrogen bond acceptors) hydrogen bonded (HB or H-bond) complexes in this article. Although C-H center dot center dot center dot Y interactions have been recognized as H-bonding interactions for quite some time, they have not been investigated spectroscopically until recently. Recent results indicated that unlike the conventional hydrogen bond, C-H center dot center dot center dot Y H-bond has interesting spectroscopic characteristics, i.e. it shows both red as well as blue shift in C-H stretching frequency upon H-bond formation. This review presents examples of red, blue, and zero shifted C-H center dot center dot center dot Y H-bonds investigated in our laboratory that were characterized using laser-based IR and UV spectroscopic techniques applied to the cold isolated molecular complexes formed under supersonic expansion conditions. Along with spectroscopic information, ab initio/DFT-predicted geometry optimized structures of various conformers, harmonic frequency calculations of the optimized structures, and a number of properties such as electron densities at the bond critical points, orbital interaction energies, binding energies of the C-H center dot center dot center dot Y bound complexes are also summarized for better understanding of this type of H-bond. Not only the spectroscopic shift in C-H stretching frequency, but also the role of C-H center dot center dot center dot O H-bonds in microsolvation of several organic molecules has been highlighted. It has been found that depending upon activation of C-H moiety, C-H center dot center dot center dot Y H-bonds can provide primary or secondary stabilization for the growth of the primary solvation shell around organic molecules.