The intriguing mass transport properties of carbon nanotubes (CNTs) have received widespread attention, especially the rapid transport of water through CNTs due to their atomically smooth wall interiors. Extensive research has been dedicated to the comprehension of various aspects of water flow in contact with CNTs, the most prominent ones being the studies on slip and flow rates. Experimental and computational studies have confirmed an enhanced water flow rate through this graphitic nanoconfinement. However, a quantitative agreement has not yet been attained. These disparities coupled with incomplete knowledge of the mechanisms of water transport at nanoscale regimes are hindering the possibilities to integrate CNTs in numerous nanofluidic applications. In the present review, we focus on the slip and flow rates of water through CNTs and the factors influencing them. We discuss the key sources of discrepancies in water flow rate and suggest directions for future study.