The basic framework and - conceptual understanding of the metallurgy of Ti alloys is strong and this has enabled the use of titanium and its alloys in safety-critical structures such as those in aircraft and aircraft engines. Nevertheless, a focus on cost-effectiveness and the compression of product development time by effectively integrating design with manufacturing in these applications, as well as those emerging in bioengineering, has driven research in recent decades towards a greater predictive capability through the use of computational materials engineering tools. Therefore this paper focuses on the complexity and variety of fundamental phenomena in this material system with a focus on phase transformations and mechanical behaviour in order to delineate the challenges that lie ahead in achieving these goals. (C) 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.