The neural dynamics of subjectivity (NDS) approach to the biological explanation of consciousness is outlined and applied to the problem of inferring consciousness in animals phylogenetically distant from ourselves. The NDS approach holds that consciousness or felt experience is characteristic of systems whose nervous systems have been shaped to realize subjectivity through a combination of network interactions and large-scale dynamic patterns. Features of the vertebrate brain architecture that figure in other accounts of the biology of consciousness are viewed as inessential. Deep phylogenetic branchings in the animal kingdom occurred before the evolution of complex behavior, cognition, and sensing. These capacities arose independently in brain architectures that differ widely across arthropods, vertebrates, and cephalopods, but with conservation of large-scale dynamic patterns of a kind that have an apparent link to felt experience in humans. An evolutionary perspective also motivates a strongly gradualist view of consciousness; a simple distinction between conscious and nonconscious animals will probably be replaced with a view that admits differences of degree, perhaps on many dimensions.