Decision analysis frameworks based on decision trees are widely used due to their expressive power at presenting the details of a decision problem. However, because the size of decision trees scales exponentially with the number of variables, they become unwieldy for even medium-sized decision problems involving multiple objectives and more than a few chance nodes, limiting ease of specification, visual representation and adaptability to change. We present influence diagrams — extensions of Bayesian networks — as alternatives to decision trees for scalable decision analysis that are only recently seeing adoption in clinical practice. Influence diagrams represent transparent decision-analytic models that can facilitate conceptual planning, reasoning, criticism, alteration and reporting, and can complement decision trees for guiding evidence-based decision-making. The Bayesian network, directed probabilistic graphical model, underlying an influence diagram can be learnt from data without relying on manual elicitation, which can be useful in resource-constrained settings. Due to their local factorization, influence diagrams scale linearly with the number of variables and provide simple, intuitive representations of decision problems. They extend naturally to sensitivity and value of information analyses, and graphical criteria can be used to reduce the complexity of decision rules through independencies in the network, and to combine knowledge from multiple sources. We describe ways to generate and solve influence diagrams, software for working with them, and applications to cost-effective analysis and mental health research.