Most influence networks are depicted as nodes and links operating in the manner of a feed-forward neural network where both nodes and links appear to be homogenous in their nature. Experience has shown that not only do these networks fail to deal adequately with reality, but also that practitioners struggle to understand why. This paper addresses this challenge by examining the rich, multi-level and multi-modal nature of influence networks and proposes an approach drawing inspiration from complexity science - leading to multiperspective techniques which enable influence networks to be used to more effectively to capture, visualise and understand complex situations, so providing insights to support effective decision-making. The paper gives evidence (from a case study looking at the provision of affordable housing in the UK) which illustrates how the techniques have been employed and what benefits accrued.