Inferring cause-effect relationships from observations is one of the fundamental challenges in natural sciences and beyond. Due to the technological advances over the last decade, the amount of observations and data available to characterize complex systems and their dynamics has increased substantially, making scientists face this challenge in many different areas. Specific examples of general importance include seismicity as well as nerve cell cultures and even the brain. In this talk, I will discuss new methods from nonlinear sciences and complex network theory to infer causal interactions and characterize spatio-temporal clustering of point processes with a particular focus on the aforementioned applications. In particular, I will present a method that identifies triggering relationships between earthquakes such that seismicity can be described by triggering cascades and mapped to a complex network. This novel approach allows one to tackle many open questions related to earthquakes and seismicity.