We present a novel iterative extraction model, IterX, for extracting complex relations, or templates, i.e., N-tuples representing a mapping from named slots to spans of text within a document. Documents may feature zero or more instances of a template of any given type, and the task of template extraction entails identifying the templates in a document and extracting each template’s slot values. Our imitation learning approach casts the problem as a Markov decision process (MDP), and relieves the need to use predefined template orders to train an extractor. It leads to state-of-the-art results on two established benchmarks – 4-ary relation extraction on SciREX and template extraction on MUC-4 – as well as a strong baseline on the new BETTER Granular task.