This handbook chapter covers the existing theoretical literature on social preference and social welfare under risk (i.e., when probability values enter the data of the situation) and uncertainty (i.e., when this is not the case and only subjective probability assessments can be formed). Section 1 sets the stage historically by contrasting classical social choice theory and welfare economics, which are restricted to the certainty case, with Harsanyi's pathbreaking attempt at extending these fields to the risk case. Section 2 reviews the work, both ancient and recent, stemming from Harsanyi's Impartial Observer Theorem. Section 3 does the same job for Harsanyi's Social Aggregation Theorem and discusses Sen's objections against the utilitarian relevance of either theorem. Section 4 explains why the Social Aggregation Theorem does not carry through from risk to uncertainty, a major conundrum that can also be expressed as a clash between ex ante and ex post welfare assessments; the proposed solutions are covered, including some very recent ones. Section 5 explains that equality, like social welfare, can be defined either ex ante or ex post, and using a basic example by Diamond, that these two definitions clash with each other. Section 6 covers the main solutions that egalitarian writers have given to this problem, again including some very recent ones.