'Sentience' sometimes refers to the capacity for any type of subjective experience, and sometimes to the capacity to have subjective experiences with a positive or negative valence, such as pain or pleasure. We review recent controversies regarding sentience in fish and invertebrates and consider the deep methodological challenge posed by these cases. We then present two ways of responding to the challenge. In a policy-making context, precautionary thinking can help us treat animals appropriately despite continuing uncertainty about their sentience. In a scientific context, we can draw inspiration from the science of human consciousness to disentangle conscious and unconscious perception (especially vision) in animals. Developing better ways to disentangle conscious and unconscious affect is a key priority for future research.