This article reviews the methods employed in modelling the various aspects of mobility of screw dislocations in the body-centred cubic (BCC) structure. The behaviour of straight dislocation cores at 0 K has been well-understood following the application of traditional 2-D atomistic simulation in the past few decades. Kink-pair activation at . non-zero temperatures has been classically treated by Volterra-type line tension models, but these have been superseded in recent years by a semi-continuum approach based on the Peierls-Nabarro framework. The use of 3-D atomistic simulation techniques in studying kink-pair related problems is also emerging. There is now the prospect that engineering-oriented phenomena such as brittle-to-ductile transition and the strain-rate sensitivity of deformation textures in BCC metals can be investigated at a more fundamental level involving dislocation core behaviour. This article reviews the methods employed in modeling the various aspects of mobility of screw dislocations in the body-centered cubic (BCC) structure. The behavior of straight dislocation cores at 0 K has been well-based following the application of traditional 2-D atomistic non-zero temperatures has been classically treated by Volterra-type line tension models, but these have been superseded in recent years by a semi-continuum approach based on the Peierls-Nabarro framework The use of 3-D atomistic simulation techniques in studying kink-pair related problems is also emerging. There is now the prospect that engineering-oriented phenomena such as brittle-to-ductile transition and the strain-rate sensitivity of deformation textures in BCC metals can be investigated at a more fundamental level involving dislocation core behavior.