Odonates are insects. That means they have the typical insect basic anatomy: head or caput, chest or thorax and abdomen. Also like any other insect, they have six legs, connected to the thorax. And like any other winged insect, their wings have six main veins that lead from the body into each wing.

Each part is now separately discussed:
 

The caput consists of the eyes, mandibles, face, antennae and the back of the head.
Odonates have two types of eyes: the "real" eyes or oculi and the ocelli. The real eyes consist of 10- to 30 thousand facets. They are small and clearly separated (Zygoptera)or very large (Anisoptera) and touch on top of the head (Anisoptera except for the Gomphidae).
The ocelli are very small eyes, odonates have three of them. They are not used to observe the environment with, but only to distinct light and dark. The ocelli are clustered on a small triangular lump: the vertex.
The mandibles are quite complex and consist of the upper and lower lips (labrum and labium respectively), surrounding the mouth with the upper jaws (mandibulae) and lower jaws (maxillae). The labrum or upper lip is connected to the face. This face, located at the front of the caput, consists of the clypeus and the frons.
The back of the head, called occiput,is reduced to a small triangle by the non-Gomphid Anisoptera, but clearly visible by the Gomphids and Zygoptera.
 

The thorax of odonates consists of three segments: the prothorax, mesothorax and metathorax. The first segment or prothorax, located at the front of an odonate’s body, is small and connects the head to the body. To this segment, the first pair of legs is connected.
The upper part of the prothorax is visible from above and is called pronotum. The pronotum of female Zygoptera has a typical shape, which is different for each species. This makes determination possible, even for very young or unusually coloured individuals.
Mesa- and metathorax have grown together and difficult to distinguish, and are therefore often considered as one single segment, simply called synthorax. The synthorax is almost completely filled with the wing muscules. The synthorax can be divided into the shoulders or mesepisternum, the left and right sides (pleurae), sternum (bottom side) and backside (terga). The terga is located between the wings, the sternum between the left and right middle and hind legs.
On each side of the thorax are two breathing openings or stigmae, one located on the metathorax and one on the prothorax.
 

Odonate legs consist of eight segments; from the body downwards:
The hip or coxa, which connects the leg to the body;
The trochanter, a small joint;
The femur or thigh;
The tibia or shin;
three tarsi and a small, two-pointed hook called unguis, together the foot.
Odonates are almost unable to walk, they use their middle and hind legs (and sometimes also their front legs) to sit on stones, sand, trees or plants. But most of all, the legs are a perfect catching device, aimed to the front. Femurs and tibiae are hairy, so they don’t loose grip.
 

Odonates have four membranous wings. Each wing is directly connected to it’s own wing muscle. That means each wing can be controlled individually. That is why the wing beat of odonates is relatively slow: only about 20 to 40 beats per second, versus more than 1000 beats per second for some mosquito species, and why they fly so well: dragonflies can fly backwards, vertically up- and downwards and even sidewards. And the slow wing beat doesn’t seem to bother them breaking flight records: large dragonflies were clocked flying 54 kilometres per hour for short times. That makes them the fastest insects on earth!
Damselflies are much slower and weaker flyers: they don’t fly very much and can usually be found sitting on plants.
Each wing has six main veins. The front vein is called the costa, working to the back the other main veins are called subcosta, radius, media, cubitus and analis.

Halfway each wing there’s a small bend in the costa, called nodus. On this place, the subcosta ends at a crossvein. More to the tip of the wing, there’s another remarkable place, called pterostigma or wing spot. This pterostigma is usually dark coloured, sometimes however it’s bright red, yellow or white. It gets it’s final colour after some days after the emergence. The colour is caused by the blood fluid in the veins. Odonates can just see their own pterostigma, that way they can see and adjust the pose of the wings during flight.
The pterostigmas of Calopterygidae are veined and not surrounded by thicker veins. That’s called a pseudo-pterostigma.
The difference between Anisoptera and Zygoptera is clearly visible in the shapes of the wings: Zygoptera have hind wings shaped equally to the front wings, with only two antenodal crossveins (veins perpendicular to the costa, situated at the front of each wing). Anisoptera have slim front wings but their hind wings are much broader at the base. Furthermore, there is a small intransparent membran in the base of each wing, called membranula.
For a few genera in Europe (Aeshna, all Gomphidae, Cordulegaster, the Corduliidae and Macromia), sexing is quite easy when observing the hind wings: females have a rounded hind wing base, while males have a 90 degrees angle in their hind wing base.
 

The abdomen of odonates, which consists of 10 segments plus the rudiment of an 11th segment, is remarkably long and slim, rarely very broad and short. The abdomen houses the internal organs and the genitalia. It also acts as a steer and helps keeping balance in flight.
Segment 1 is very short and not visible from above. Segment 3 to 7 are quite long, the others are shorter. Segment 10 carries a few projections called anal appendages.
Each segment consists of an upper side or tergite and a bottom side or sternite, connected by pleurites at the flanks. The tergites are musch bigger and harder than the sternites, which are quite weak and flexible.
The genitalia of odonates are very complex. Males have their sperm production organ in the 9th segment (like any other insect) but their copulation organ (that acts as a penis) is located underneath segment 2. These organs are not interconnected, so the male has to transfer his sperm from the producing organ to the penis before the actual copulation takes place!
The penis (called ligula) is an important characteristic for the recognition of male Zygoptera in case of doubt. For libellulidae (a group of Anisoptera), the hamulus can be used for species recognition. The hamulus is a set of hooks situated at the sternite of segment 2, used to hold the female’s genitalia during copulation.
For the female, genitalia are located underneath the abdomen between segment 8 and 9. Zygoptera and some Anisoptera (Aeshnidae and Cordulegaster) have an ovipositor, surrounded by valvae. An ovipositor is used to stick eggs in plants, wood or mud. These species are called endofytic. Species that don’t have an ovipositor (exofytic) simply drop their eggs into the water.

At the back of segment 10, at the tip of the abdomen, the appendages are located. These are especially clearly visible at male odonates.
Male Zygoptera have two pairs of anal appendages: the upper appendages (appendices superiores) and the lower appendages (appendices inferiores). Anisoptera males only have upper appendages, plus one single small knob that is also called lower appendage.
Female odonates only have very small appendages, which are functionless. These are called cerci.
The appendages of male odonates have an important function during the copulation: with these appendages, the males hold the females behind the eyes (Anisoptera) or at the back edge of the prothorax (Zygoptera). The shape of the appendages of a species is typical for that species and corresponds with the shape of the female’s prothorax (Zygoptera), which prevents bastardising. For Anisoptera, the hamulus prevents bastardising: only female’s genitalia of the same species fit. Very rarely however, bastardising occurs.