Complexity science has seen increasing interest in the recent years. Many engineers have discovered that traditional methods come to their limits when coping with complex adaptive systems or autonomous agents. To find alternatives, complexity science can be applied to engineering, resulting in a quickly growing field, referred to as complexity engineering. Most current efforts come either from scientists who are interested in bio-inspired methods and working in computer science or mobile robots, or they come from the area of systems engineering. This article is the second part of a set of two articles on this topic; the first one reviewed the definitions of the most important concepts such as emergence and self-organisation from an engineer's perspective, and analysed different types of nature-inspired technology. This article provides a survey of the currently existing approaches to complexity engineering. In the end, challenges ahead are indicated.