The common envelope interaction between a giant star and a stellar or substellar companion is at the origin of several compact binary classes, including the progenitors of Type Ia SN. A common envelope is also what will happen when the Sun expands and swallows its planets as far out as Jupiter. The basic idea and physics of the common envelope interaction has been known since the 1970s. However, the outcome of a common envelope interaction - what systems survive and what their parameters are - depends sensitively on the details of the engagement. To advance our knowledge of the common envelope interaction between stars and their stellar and substellar companions, we have carried out a series of simulations with Eulerian, grid-based and Lagrangian, smoothed particle hydrodynamics codes between a 0.88-M⊙, 85-R⊙, red giant branch star and companions in the mass range 0.1-0.9 M⊙. In this contribution, we will discuss the reliability of the techniques, the physics that is not included in the codes but is likely important, the state of the ejected common envelope, and the final binary separation. We also carry out a comparison with the observations. Finally, we discuss the common envelope efficiency parameter, α and the survival of planets.