The rapid growth of computation-intensive applications like augmented reality, autonomous driving, remote healthcare, and smart cities has exposed the limitations of traditional terrestrial networks, particularly in terms of inadequate coverage, limited capacity, and high latency in remote areas. This chapter explores how integrated terrestrial and non-terrestrial networks (IT-NTNs) can address these challenges and enable efficient computation offloading. We examine mobile edge computing (MEC) and its evolution toward multiple-access edge computing, highlighting the critical role computation offloading plays for resource-constrained devices. We then discuss the architecture of IT-NTNs, focusing on how terrestrial base stations, unmanned aerial vehicles (UAVs), high-altitude platforms (HAPs), and LEO satellites work together to deliver ubiquitous connectivity. Furthermore, we analyze various computation offloading strategies, including edge, cloud, and hybrid offloading, outlining their strengths and weaknesses. Key enabling technologies such as NOMA, mmWave/THz communication, and reconfigurable intelligent surfaces (RIS) are also explored as essential components of existing algorithms for resource allocation, task offloading decisions, and mobility management. Finally, we conclude by highlighting the transformative impact of computation offloading in IT-NTNs across diverse application areas and discuss key challenges and future research directions, emphasizing the potential of these networks to revolutionize communication and computation paradigms.