In a metaphorical sense a thing is complex if it comprehends a magnitude of homogeneous or different things. However, it depends on the kind of comprehension, if we conceive something that consists of many things as complex or not. It is perhaps most distinctive for complex phenomena that their properties and behaviour are not reducible to the properties and behaviour of their elements. This poses some challenging metaphysical problems. The articles in this anthology do not follow a leitmotif -- aside from that all of them have a look at complexity problems in different areas of scientific research and show in which ways the challenges of complexity can be answered.