Do nonhuman animals (henceforth, animals) have emotions, and if so, are these similar to ours? This opinion piece aims to add to the recent debate about this question and provides a critical re-evaluation of what can be concluded about animal and human emotions. Emotions, and their cognitive interpretation, i.e., feelings, serve important survival functions. Emotions, we believe, can exist without feelings and are unconsciously influencing our behavior more than we think, and possibly more so than feelings do. Given that emotions are expressed in body and brain, they can be inferred from these measures. We view feelings primarily as private states, which may be similar across closely related species but remain mostly inaccessible to science. Still, combining data acquired through behavioral observation with data obtained from noninvasive techniques (e.g., eyetracking, thermography, hormonal samples) and from cognitive tasks (e.g., decision-making paradigms, cognitive bias, attentional bias) provides new information about the inner states of animals, and possibly about their feelings as well. Given that many other species show behavioral, neurophysiological, hormonal, and cognitive responses to valenced stimuli equivalent to human responses, it seems logical to speak of animal emotions and sometimes even of animal feelings. At the very least, the contemporary multi-method approach allows us to get closer than ever before. We conclude with recommendations on how the field should move forward.