Three types of concern for animal welfare are widely held: Animals should feel well, they should function well, and they should lead natural lives. The paper deals with a well-known answer to the question of why such concerns are morally appropriate: Human beings have direct duties towards animals, because animals are beings that can flourish, the flourishing of animals is intrinsically or inherently valuable, and that which is conducive to their flourishing is a legitimate object of moral concern. Looking for a tenable conception of direct duties towards animals, the following questions are discussed: What should we take it to mean that "animal flourishing is intrinsically or inherently valuable?'' Under what conditions does a living being's ability to flourish create direct duties towards this being? Is awareness or sentience required for there to be direct duties towards a living being? Does such a requirement imply that moral concerns for animals would be limited to their feeling well, or does it also give way to having moral concerns for their functioning well and leading natural lives? Can one take into account considered judgements that claim that towards different animals we have moral duties that differ in kind and/or strength? If environmental ethics cannot be based on the conception of direct duties here discussed, should one draw a distinction between duties towards ourselves, our fellow human beings, or animals, and duties regarding plants, or collective entities such as populations, species, and ecosystems?