This paper explores the effect of unhedgeable background risks such as mortality and labour risks (such as wages and turnover) on pension funding and finance. We explore the literature on the economics and finance of background risk, and discuss its applicability to pensions. Most of the results in economics apply to the special case of additive background risk, which is part of, but not all of, the background risk faced by pension funds. We develop three illustrative models and show the impact of background risk on pension funding and asset allocation. We find that the asset allocation and funding decisions of pension plans in general change with the introduction of background risk, in some cases significantly. We also explore implications of background risk for fair value calculations.