Multicriteria Portfolio Analysis spans several methods wh ich typically employ build on MCDA to guide the selection of a subset (i.e., portfolio) of available objects, with the aim of maximising the performance of the resulting portfolio with regard to multiple criteria, subject to the requirement that the resources consumed by the portfolio does not exceed the availability of resources and, moreover, satisfies other relevant constraints as well. In this chapter, we present a formal model of this selection pro blem and describe how this model can present both challenges (e.g. portfolio value may, due to the interactions of elements, depend on project-level decisions in complex and non-additive ways) and opportunities (e.g. triage rules can be used to focus elicitation on projects which are critical) for value assessment. We also survey the application of Portfolio Decision Analysis in several domains, such as allocation of R&D expenditure, military procurement, prioritisation of healthcare projects, and environment and energy planning, and conclude by outlining possible future research directions.