Extending the weldability of novel materials, and improving the weld quality by tailoring weld microstructures are key factors to obtain the welding techniques demanded in the modern manufacturing industries. This can be done, for example, by feeding chemical elements from a consumable wire into the weld pool during welding. The mixing of chemical components in the weld pool and the resulting post-solidification weld microstructures are influenced by weld pool hydrodynamics. Weld pool hydrodynamics is known to be primarily driven by Marangoni forces acting at the free liquid surface, i.e by tangential gradients in surface tension along the liquid surface due to pronounced lateral gradients in temperature and surface active element concentration. In this research, we develop a Computational Fluid Dynamics model to study steel weld pool hydrodynamics during conduction mode laser spot welding. It is concluded that free surface deformations and instabilities have a strong impact on the fluid flow and heat transfer in weld pools, and should therefore be accounted for in weld pool simulations. With increasing the surface active element concentration and laser power, the weld pool flow becomes highly unstable and can no longer be accurately modeled with a flat surface assumption. More accurate predictions of weld pool physics can be made if the free surface, solidification stage, and three-dimensionality are taken into account. This reduces the need for the use of unphysical parameter fittings widely reported in literature.