The Arrhinias consist of three groups of malformations: the Total Arrhinias (T-AR), the Hemi-Arrhinias (H-AR, often called Hemi-Nasal Ageneses) and the Proboscis Lateralis (P.L.) This work deals with 51 cases of Arrhinias gathered within 35 years (8 T-AR, 25 H-AR, and 18 P.L): their anatomy, clinical signs, and some indications for treatment; but it does not extend to a discussion for their etiopathology. However, the T-AR and the H-AR represent ageneses, whereas the P.L represents a dysgenesis. The anomalies common to the three groups of Arrhinias are many: the agenesis of the nasal bones, the telecanthus which is often in contrast to the hypo-telorbitism, the obstruction of the naso-lacrimal passage, the ectasia of the lacrimal sac with an erosion of the inferomedial angle of the orbit, the hypopneumatization of the maxillary sinus and a small maxilla, the unerrupted canines, the flattened fronto-nasal process, the obliteration of the cribriform plate, the dysplasia in the root of the eyebrows, the transverse hypoplasia of the upper lip, the frequency of microphthalmia, colobomas of the iris and nystagmus. Cleft lip and palate are frequently associated with the Arrhinias (see Table I) and also other facial malformations, but in different proportions, according to groups. They are: cryptophtalmias, eyelid coloboma, fronto-orbital encephalocele, agenesis of the premaxilla or prolabium, microtia. (See Table II) The basic principles of the treatment are the following: In the T-AR, a nasal passage should initially be bored through the maxilla, or there should be a displacement of the two halves of the mid-face by a procedure known as "facial bipartition". This nasal passage should be epithelialized and maintained wide open to the pharynx until the nasal construction. In the H-AR, it is sufficient to create an epithelialized passage through the curtain of bone where one would expect the pyriform rim to be and carry this passage through the septum into the contralateral nasal airway. Then, regardless of the type of arrhinia, the nasal construction is carried out with a forehead flap and bone grafts. The first grafts are either iliac or tibial, and subsequent ones are generally outer table calvarial grafts harvested from the parietal region. Later, there are further procedures: a maxillary advancement, a lengthening of the central midface, the final stages of the nasal construction, the elevation of the medial canthus, and the restoration of the infero-medial angle of the orbit (but rarely an efficient lacrimal drainage). The earliest stage for surgery can be debated. A strategy for treatment is suggested. Finally, 20 brief comments are made, which are as much questions asked concerning the three groups of arrhinia and their relationship with other centro-facial and latero-facial malformations.