The SECCHI instruments aboard the recently launched STEREO spacecraft enable for the first time the continuous tracking of coronal mass ejections (CMEs) from the Sun to 1 AU. We analyze line-of-sight observations of the 24 - 25 January 2007 CMEs and fill the 20-hour gap in SECCHI coverage in 25 January by performing a numerical simulation using a three-dimensional magneto-hydrodynamic (MHD) code, the Space Weather Modeling Framework (SWMF). We show how the observations reflect the interaction of the two successive CMEs with each other and with the structured solar wind. We make a detailed comparison between the observations and synthetic images from our model, including time-elongation maps for several position angles. Having numerical simulations to disentangle observational from physical effects, we are able to study the three-dimensional nature of the ejections and their evolution in the inner heliosphere. This study reflects the start of a new era where, on one hand, models of CME propagation and interaction can be fully tested by using heliospheric observations and, on the other hand, observations can be better interpreted by using global numerical models.