The Future Internet will integrate large-scale systems constructed from the composition of thousands of distributed services, while interacting directly with the physical world via sensors and actuators, which compose the Internet of Things. This Future Internet will enable the realization of the Smart Cities vision, in which the urban infrastructure will be used to its fullest extent to offer a better quality of life for its citizens. Key to the efficient and effective realization of Smart Cities is the scientific and technological research covering the multiple layers that make up the Internet. This paper discusses the research challenges and initiatives related to Future Internet and Smart Cities in the scope of the InterSCity project. The challenges and initiatives are organized in three fronts: (1) Networking and High-Performance Distributed Computing; (2) Software Engineering for the Future Internet; and (3) Analysis and Mathematical Modeling for the Future Internet and Smart Cities. InterSCity aims at developing an integrated open-source platform containing all the major building blocks for the development of robust, integrated, sophisticated applications for the smart cities of the future.