The current status of the search and study of Blue Stragglers (BSS) in Galactic globular clusters is reviewed leading to a catalog of 425 BSS-candidates in 21 clusters. A new interpretative scenario is presented, based on the claimed detection of a BSS-progeny located on the red Horizontal Branch (HB) in the various clusters, as first suggested by Renzini and Fusi Pecci (1988, ARA&A, 26, 199) for M3. The cluster concentration and integrated luminosity are important driving parameters when considering the properties of the BSS population and HB morphology, now partially connected to each other. Implications and problems emerged within the framework of cluster stellar evolution are discussed and some speculations are presented. BSS luminosity functions (LF) are also presented and discussed. Though selection effects and poor statistics still dominate the available database, the total BSS LF shows a clear peak at M(V) approximately +3.2 and the brightest BSS are about 2.5 mag brighter than the corresponding turnoff stars. Concerning the BSS location with respect to the extension of the zero age main sequence (ZAMS) and its dependence on metallicity, the BSS sequence always has a much larger intrinsic width than expected from photometric errors and is systematically shifted towards the red with respect to the ZAMS. This redward shift appears to be slightly related with metallicity. Finally, a preliminary analysis of the population ratios between detected BSS in a cluster, N(BSS), and their claimed progeny on the HB, NB(BSP)HB, leads to N(BSS)/N(BSP)HB approximately 6.