Incremental learning refers to learning from streaming data, which arrive over time, with limited memory resources and, ideally, without sacrificing model accuracy. This setting fits different application scenarios where lifelong learning is relevant, e.g. due to changing environments , and it offers an elegant scheme for big data processing by means of its sequential treatment. In this contribution, we formalise the concept of incremental learning, we discuss particular challenges which arise in this setting, and we give an overview about popular approaches, its theoretical foundations, and applications which emerged in the last years.