The ab initio computation of molecular electronic structure - whether through density functionals or correlated wavefunctions - is very widely and successfully used for the prediction of structure, properties and reactivity. However, the application to systems where electron correlation effects are strong, for example when chemical bonds are broken, or in multiple-open-shell systems such as molecular magnets, remains a significant challenge. Standard approaches based on a single dominant configuration, which are polynomial scaling in their resource demands, do not work well when there are many equally-important configurations. More general approaches are typically factorial scaling and therefore difficult to deploy on all but very small molecules. In this talk, I will demonstrate some new approaches to this problem and discuss computational aspects of their deployment.