Both Crickets (superfamily Grylloidea) and Katydids (superfamily Tettigonioidea) belong to the order Orthoptera, suborder Ensifera and "sing" by rubbing their forewings together. Only male crickets sing, but in some katydid species, both the males and the females sing. I heard these very common insects singing every evening while I was in Costa Rica, but since they are mainly out and about at night and tend to hide in the foliage or leaf litter, I only saw a few of them while I was there.
I spotted this yellow-green katydid with gleaming red eyes lurking under a leaf in the jungle one evening.
Katydids and crickets can easily be distinguished from the related Grasshoppers (order Orthoptera, suborder Caelifera) by their long antennae, which are at least as long as their body, but often much longer as in this case. Katydids and crickets can be told apart by looking closely at their feet (tarsi), as katydids have 4-segmented feet and crickets have 3-segmented feet, but each also often has a characteristic appearance as well.
I spotted this orange cricket on a night hike through the jungle, and even though its color was unusual, I knew it to be a cricket based on its characteristic appearance alone. I did count the tarsi segments in the photo, and there were three. This colorful cricket won't be doing any singing though. It has a large ovipositor at the tip of the abdomen, and thus it is a silent female.
Since katydids and crickets use their forewings for singing, the wingless nymphs (immatures) are also silent.
I discovered this katydid nymph crawling on the mosquito netting over my bed one evening. It almost looked like it was wearing military camouflage and would have been very hard to see in the jungle, but I easily spotted it on the white netting.
To avoid predation, most species of katydids are camouflaged. Some species even look remarkably like green leaves with a leaflike coloration, shape, and even venation patterns.
I found this green katydid hiding in my bedspread one morning, where its leaflike appearance made very poor camouflage. It didn't seem to know that though and remained very still, hoping that I wouldn't see it. I picked up the katydid by its wings and tossed it outside. The frightened katydid flew a short distance into some vines and almost magically disappeared among all the green leaves. I don't know what a katydid had been doing in my bed.