Tungsten (W) and molybdenum (Mo) exhibit remarkable material properties such as high melting point, high tensile strength at elevated temperatures and low thermal expansion, which is important in many applications. However, W and Mo are prone to brittle fracture at and below room temperature. This brittle fracture preferably runs along grain boundaries (GBs), which is the weak spot of W and Mo and limits their applicability considerably. This thesis investigates the underlying reasons for the low temperature brittleness in W and Mo and offers counteracting measures by simulating GBs with ab-initio density functional theory. In the first part of this thesis, GB properties are computed and analysed for a comprehensive set of GBs in different body-centred cubic (bcc) metals. By evaluating the ratio of GB cohesion to bulk cohesion, it is shown that in comparison to other bcc metals, W and Mo feature a relatively low ratio. This indicates that the preferred fracture along GBs is intrinsic to W and Mo.The second part of this thesis explores the possibility to counteract the GB brittleness by alloying. For a comprehensive set of solutes, the segregation to GBs in W and Mo is studied and the effect on GB cohesion evaluated. By that, a set of beneficial solute elements, which increase GB cohesion, is established. In addition to treating segregation in the pristine W and Mo, the special case of the highly alloyed W-25at\%Re is investigated.