According to the Facts on File Encyclopedia of Word and Phrase Origins, written by Robert Hendrickson, the origins for this idiom are uncertain, however, he explains a theory behind it might possibly involve a cat being able to smell a rat nearby, despite not having sight of it. (source) The figurative use of this idiom is that something feels off - not quite right - but you can't quite put your finger on what it is.

This one is pretty straightforward. Old fish (not good to eat) smells fishy with bad odor caused by a chemical named trimethylamine which is released when fish begins to break down. ( source ) What it means in the figurative is that something seems suspicious or shady.

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I've alluded to smelling things already but I've never actually focused on just the actual sense of smell.  What a wondrous thing!  It gives us pleasure, it warns us away from something (I'm thinking skunks), it prompts other senses to kick in.  I love walking into a place that has coffee brewing and something baking, the smell is divine.  Sometimes the sense of smell tells me who was just in the space I have moved into - people sometimes have a very strong signature scent/smell.  Good or bad sometimes what I smell transports me to a memory of a place, a person, or an experience.  Sense of smell is one of those things that I think most of us take for granted until we don't have it any longer.  Maybe today we could pay more attention to the gift of the sense of smell and inhale the world around us.