Although it appears that box-pressed cigars are trending in the cigar industry, the fact is that they have been around for generations. These cigars have squared sides (some more squared than others) versus the classic cylindrical shaped cigars. Box-pressing cigars originated in Cuba, in efforts for manufacturers to be more efficient by packaging the cigars very tightly in flat wooden boxes for shipment. The cigars, when boxed at a higher humidity level, will take on the shape of the box as their humidity stabilizes. There are two methods of box-pressing cigars used to attain the squared appearance: standard box-pressing and trunk-pressing.
Standard box-pressing is more commonly practiced than trunk-pressing. In standard box-pressing, the classic cylindrically produced cigars are packed tightly into boxes, resulting in the shape taking on the shape of the box. The pressure from the four sides of the box presses the cigars into a shape that is between a circle and a square - a box-shape with rounded edges.
Trunk-pressing is a more elaborate, delicate, and time-consuming process, that results in cigars with a much more highly pronounced square shape. To avoid damaging or splitting the cigar wrappers, this process requires some care. Some of the old, antique presses are wooden and made with about 10 shelves, each holding about 25 cigars. Once the cigars are lined up along shelves, wooden slats are placed between cigars as they are subsequently compacted with clamps for anywhere from 30 minutes to 12 hours. After this time, the clamps are released, the cigars are turned, and pressure is re-applied to the other side for an equal amount of time.
From a Smokeasy post from September 28, 2012 (see From Seedling to Packaging - The Cigar Odyssey with Rocky Patel), Rocky Patel describes the process of box pressing cigars in this video:
As a result of the tobacco leaves being bunched even tighter together, box-pressed cigars supposedly burn longer and are more flavorful. The Padron 1964 Aniversario series was the first non-Cuban box-pressed cigars manufactured. Currently, there are some absolutely fantastic non-Cuban box-pressed cigars on the market, including (but not limited to):
601 Blue Label Maduro (Nicaragua)
AJ Fernandez San Lotano Maduro (Nicaragua)
Alec Bradley Prensado (Honduras)
Alec Bradley Vice Press (Honduras)
Arturo Fuente Añejo No. 77 "Shark" (Dominican Republic)
Carlos Toraño Exodus 1959 (Honduras)
Casa Magna Colorado Box Pressed (Nicaragua)
Illusione Epernay Le Taureau (Honduras)
Java by Drew Estate (Nicaragua)
La Aroma de Cuba Mi Amor (Nicaragua)
La Flor Dominicana Factory Press IV (Dominican Republic)
My Father Le Bijou 1922 Torpedo (Nicaragua)
Oliva Serie G (Nicaragua)
Ortega Serie D (Nicaragua)
Rocky Patel Decade 10th Anniversary (Nicaragua)
Sancho Panza (Honduras)
The "Shark" is the most interesting, as it is a torpedo that is a rounded parejo at the head and progresses to a box-shaped foot - not certain how the Fuente torcedores pulled that off! I love box-pressed cigars - my experience is that they definitely burn slower and longer, produce firm and long ashes, are quite full of flavor, have a great draw, and are very comfortable to hold in the mouth and between the fingers.