The Trends in International Mathematics and Science Study (TIMSS) measures trends in mathematics and science achievement of fourth- and eighth-grade students. TIMSS was first administered in 1995 and has been repeated every four years since then. Most recently, TIMSS 2007 was conducted in 60 countries, including 22 European countries. Measuring trends over time in student achievement while keeping the assessment relevant in a continuously evolving educational environment is a challenging endeavor requiring sophisticated statistical methods. To report mathematics and science achievement for student populations, TIMSS uses item response theory scaling together with conditioning and multiple imputation methodology. This paper describes the concurrent calibration scaling methodology (Foy, Galia, & Li, 2008) used by TIMSS to link successive assessments to a common scale, enabling the measurement of growth or decline in student achievement over time. An important feature of the TIMSS 2007 assessment was a change in the data collection design (Mullis, et al., 2005) necessitating the implementation of an additional “bridging component” to link the 2003 and 2007 assessments. This paper describes the design and implementation of the bridging study, and the steps taken to use the bridging data to establish the link between the 2003 and 2007 assessments.