Edge computing has emerged as a major disrupting technology after Cloud computing to fill in the computational and infrastructural gaps in IoT and Mobile Cloud computing. Indeed, IoT and Mobile Cloud computing are based on rather direct connection of devices to Cloud servers and data centers, such as through gateways, and are not able, due to round trip time, to cope with demanding requirements of real-time applications for low latency, critical decision making, increased security, support to mobility, etc. The aim of computing at Edges of Internet is to alleviate the burden of IoT data stream processing to the Cloud computing by pushing part of the computations, storage, reasoning and intelligence to the Edges of the Internet, close to where data is generated and to end-users. In this introductory chapter we discuss the vision of Edges of Internet as a computing fabric to support real-time applications, high performance computing, big data and big data stream processing at large scale. The ever growing number of compute nodes (from small to large), of fast connectivity (supported by 5G technologies) and of data storage (mini/nano data centers) provide the basis to achieve the vision of computing fabric. The challenges of achieving such vision due to a number of complexities are also discussed.