Most existing researches on relation extraction focus on binary flat relations like BornIn relation between a Person and a Location. But a large portion of objective facts described in natural language are complex, especially in professional documents in fields such as finance and biomedicine that require precise expressions. For example, “the GDP of the United States in 2018 grew 2.9% compared with 2017” describes a growth rate relation between two other relations about the economic index, which is beyond the expressive power of binary flat relations. Thus, we propose the nested relation extraction problem and formulate it as a directed acyclic graph (DAG) structure extraction problem. Then, we propose a solution using the Iterative Neural Network which extracts relations layer by layer. The proposed solution achieves 78.98 and 97.89 F1 scores on two nested relation extraction tasks, namely semantic cause-and-effect relation extraction and formula extraction. Furthermore, we observe that nested relations are usually expressed in long sentences where entities are mentioned repetitively, which makes the annotation difficult and errorprone. Hence, we extend our model to incorporate a mentioninsensitive mode that only requires annotations of relations on entity concepts (instead of exact mentions) while preserving most of its performance. Our mention-insensitive model performs better than the mention sensitive model when the random level in mention selection is higher than 0.3.