Polymerases and ribosome are molecular machines which perform three important biological functions. Like cytoskeletal motors, each of these moves along a track using chemical energy for performing mechanical work. Moreover, it decodes genetic information chemically-encoded in the sequence of the subunits of the track. Furthermore, it polymerizes a macromolecule (DNA, RNA or protein) using the required subunits in a sequence that is dictated by the sequence of subunits of a template which serves also as its track for translocation. Enormous progress has been made in the last decade in understanding the structure and dynamics of these molecular machines using a combination of X-ray crystallography, cryo-electron microscopy, single-molecule imaging and manipulation. In recent years, we have developed models of these machines capturing the key features of their structure and dynamics to gain a quantitative understanding of their operational mechanism. We have also investigated the traffic-like collective movement of ribosomes simultaneously on the same mRNA track (and similar traffic of RNA polymerases on a DNA). We have also suggested new experiments for testing our theoretical predictions on the stochastic translocation-and-pause kinetics of a single motor as well as on their collective spatio-temporal organization.