Potential energy surfaces (PES) for the reactions X + HD -2 ⇌ 2 HX + D -3 ⇌ 3 DX + H, where X is a halogen, are reviewed. Reactions involving two or three halogen atoms are also discussed. Many calculations have been performed using semiempirical variations of the London PES equation (LEPS methods) which was originally developed for treating the H + H2 reactions. There are many problems in extending this treatment to the halogen reactions and some of these, including excited electronic states, p Orbitals, relativistic effects, and possibilities for nonlinear transition states, are mentioned. Furthermore, the London equation and its variations are found to be pathologically sensitive to the input coulomb ratios, both when these are semiempirical and when they are theoretical. The use of transition state theory to relate postulated potential energy surfaces to experimental data causes further errors, especially for reaction 2 when X = Br or I. More importantly, rate data in thermal bulk-gas systems are insufficient to determine most PES features. Experiments which measure scattering angles and internal energies of the products combined with single-collision scattering theory interpretations will provide more critical conditions on trial PES topography. A priori calculations of potential energy surfaces will also be useful in some cases. For some cases, features such as reaction barrier height and location and width of the barrier can presently be assigned satisfactory qualitative values. However, the depth and even the existence of potential wells in many of the systems is uncertain. In cases where wells are known to exist, it is found that the semiempirical LEPS methods fail to reproduce observed force constants. The transferability of the Sato parameters in the LEPS methods from system to system is not promising, but it is possible that a single set of Sato parameters will serve well for both reactions 2 and 3 for a single X. New transition state isotope effects for reaction -2 with X = Br are presented. Although they give results closer to experimental values than do previous calculations, it is shown why little confidence can be placed in the absolute accuracy of the PES leading to these predictions.