The long-term goal of artificial intelligence (AI) is to make machines learn and think like human beings. Due to the high levels of uncertainty and vulnerability in human life and the open-ended nature of problems that humans are facing, no matter how intelligent machines are, they are unable to completely replace humans. Therefore, it is necessary to introduce human cognitive capabilities or human-like cognitive models into AI systems to develop a new form of AI, that is, hybrid-augmented intelligence. This form of AI or machine intelligence is a feasible and important developing model. Hybrid-augmented intelligence can be divided into two basic models: one is human-in-the-loop augmented intelligence with human-computer collaboration, and the other is cognitive computing based augmented intelligence, in which a cognitive model is embedded in the machine learning system. This survey describes a basic framework for human-computer collaborative hybrid-augmented intelligence, and the basic elements of hybrid-augmented intelligence based on cognitive computing. These elements include intuitive reasoning, causal models, evolution of memory and knowledge, especially the role and basic principles of intuitive reasoning for complex problem solving, and the cognitive learning framework for visual scene understanding based on memory and reasoning. Several typical applications of hybrid-augmented intelligence in related fields are given.