The transit of coronal mass ejections (CMEs) from the Sun to 1 AU lasts on average one to five days. As they propagate, CMEs interact with the solar wind and preceding eruptions, which modify their properties. In the past ten years, the evolution of CMEs in the inner heliosphere has been investigated with the help of numerical simulations, through the analysis of remote-sensing heliospheric observations, especially with the SECCHI suite onboard STEREO, and through the analysis of multi-spacecraft in situ measurements. Most studies have focused on understanding the characteristics of the magnetic flux rope thought to form the core of the CME. Here, we first review recent work related to CME propagation in the heliosphere, which point towards the need to develop more complex models to analyze CME observations. In the second part of this article, we review some recent studies of CME-CME interaction, which also illustrate the complexity of phenomena occurring in the inner heliosphere.