The New Robotic Telescope (NRT) is a new UK/Spain 4-m optical telescope on La Palma. When complete it will be the world's largest and fastest, fully autonomous optical observatory and is being designed to address the coming era of time-domain and transient astrophysics. We summarise the planned software architecture, presented as a complete, coordinated observatory system from telescope axis control, through intelligent, automated scheduling, up to the user interfaces available at astronomers' home desks. We have adopted a blend of proven software from existing telescopes with developing new systems suited to the telescope's unique requirements and to modern web-based, collaboration models. We pay particular attention to aspects of the software stack that distinguish this project and enable the unsupervised, autonomous science operations in which observers around the globe can specify and monitor their observing requests intra-night without needing any support from observatory staff.