Domestic dogs (Canis familiaris) have excellent olfactory processing capabilities that are utilized widely in human society e.g., working with customs, police, and army; their scent detection is also used in guarding, hunting, mold-sniffing, searching for missing people or animals, and facilitating the life of the disabled. Sniffing and searching for odors is a natural, species-typical behavior and essential for the dog's welfare. While taking advantage of this canine ability widely, we understand its foundations and implications quite poorly. We can improve animal welfare by better understanding their olfactory world. In this review, we outline the olfactory processing of dogs in the nervous system, summarize the current knowledge of scent detection and differentiation; the effect of odors on the dogs’ cognitive and emotional processes and the dog-human bond; and consider the methodological advancements that could be developed further to aid in our understanding of the canine world of odors.