My dissertation seeks to understand our concept of moral claim-rights---rights of one person against another. It achieves this understanding by doing two main things: analyzing our concept of moral claim-rights in terms of our concept of moral duties; and discerning the role in our moral thinking of our concept of moral duties. Along the way, various views of, and issues surrounding, these two concepts are considered. ;Roughly, my view of our concept of moral claim-rights is this: X has a moral (...) claim-right against Y that Y do A if and only if whether Y has a moral duty to do A depends on whether X would desire that Y do A were X instrumentally rational and in possession of full relevant information. Suppose Boris has promised Alice that he will paint her house. She thus has a moral claim-right against Boris that he do so. Does this mean Boris has a moral duty to paint her house? No, since Alice might not desire that Boris paint it . ;Generally, my view of the role of our concept of moral duties in our moral thinking is that, as we think, moral duties are some, but not all, of the considerations bearing upon what one ought morally to do. More specifically, "ought morally" has a two-filter structure---an agent ought morally to perform one or another of those actions available to her which survives two successive stages of filtering. The first stage of filtering involves trading-off considerations of moral duty against those of overall goodness, while the second stage involves trading-off considerations of overall goodness against those of personal interest. In illustration of the first stage, where moral duties are involved, suppose that Alice can make some net contribution to the overall good by slapping Boris. Since Alice has a moral duty not to slap Boris, it is morally impermissible for her to do so unless the contribution she can make to the overall good is quite large. (shrink)