  We summarize the motivations for and the status of the calculation of the $W
+$ heavy quark production process in $p \bar p$ colliders to Next-to-Leading
Order in QCD. This process can be used to constrain the strange quark
distribution function at high $Q^2$ at the Tevatron, and also to study the
bottom content of $W+1$~jet events. In addition, when crossed, the calculation
essentially describes the single top quark production process to
Next-to-Leading Order in QCD.
