The acquisition, digital representation and interaction of cultural heritage (CH) assets is of high interest for an accurate documentation of our cultural legacy. Detailed studies demand more information on the assets apart from the mere visual appearance or even shape of objects. In this regards, some research works can be found that combine shape with other kind of data, such as radiometric (e.g., IR, thermal radiation, etc.) or semantic information, leading to multi-Dimensional (mD) virtual objects. In this chapter, we review the state of the art of different techniques to deal with mD acquisition of CH tangible assets. We also discuss some representation (e.g., visual, sonic, etc.) and interaction approaches to enhance the value of CH by means of the technologies of virtual reality (VR) and augmented reality (AR), considering also the application of these techniques to tourism. Finally, we also point out some current needs and technological barriers that need to be tackled by the research community regarding the acquisition and dissemination of heritage.