While plant and insect brains may not be as complicated as human ones, they’re very complex and likely resemble our processes more than we commonly believe. From Oliver Sacks in the New York Review of Books:

“Where Aplysia has only 20,000 neurons distributed in ganglia throughout its body, an insect may have up to a million nerve cells, all concentrated in one brain, and despite its tiny size may be capable of extraordinary cognitive feats. Thus bees are expert in recognizing different colors, smells, and geometric shapes presented in a laboratory setting, as well as systematic transformations of these. And of course, they show superb expertise in the wild or in our gardens, where they recognize not only the patterns and smells and colors of flowers, but can remember their locations and communicate these to their fellow bees.

It has even been shown, in a highly social species of paper wasp, that individuals can learn and recognize the faces of other wasps. Such face learning has hitherto been described only in mammals; it is fascinating that a cognitive power so specific can be present in insects as well.

We often think of insects as tiny automata—robots with everything built-in and programmed. But it is increasingly evident that insects can remember, learn, think, and communicate in quite rich and unexpected ways. Much of this, doubtless, is built-in—but much, too, seems to depend on individual experience.

Whatever the case with insects, there is an altogether different situation with those geniuses among invertebrates, the cephalopods, consisting of octopuses, cuttlefish, and squid. Here, as a start, the nervous system is much larger—an octopus may have half a billion nerve cells distributed between its brain and its ‘arms’ (a mouse, by comparison, has only 75 to 100 million). There is a remarkable degree of organization in the octopus brain, with dozens of functionally distinct lobes in the brain and similarities to the learning and memory systems of mammals.”