The DeLorean car originally came with two different types of windshields during the course of original production.
The first, installed on 1981 models up to approximately VINs ending in 02711, is identifiable by the embedded radio antenna. Poor reception was reportedly the reason this was eliminated by the factory.
From approximately VIN 02712, only windshields without an antenna were fitted, and the cars were intended to come with one of three types of antennas (see article on Antennas in Electrical section).
Sometime in the early 1980s, stocks of windshields with antennas were exhausted as "spare parts" and only the non-antenna windshield was available. Many cars that originally were fitted with antenna windshields were forced to use a non-antenna windshield and fit an external antenna to the car.
In 2009, supplies of NOS (new old stock) windshields were exhausted entirely, and DMC (Texas) contracted with a glass maker to tool up and produce new stocks. These are now available in three different varieties:
All three are imprinted in the lower left corner (when seated in the car) with the DMC logo and manufacturer's marks.

In 2022, we worked with our supplier to add a "frit" pattern to the windshield design. Frit patterns have been used on cars for decades and for the purposes of the DeLorean, this design change serves a couple different purposes. Adding the frit to the sides and bottoms helps to obscure any excess adhesive that might be visible after installation and the shade band area at the top of the windshield makes the area where the glass, underbody and leading edge of the front headliner are often visible and unsightly.

Replacement of the windshield is usually best left to a professional glass shop, although an owner can often save a bit of money by preparing for the work (remove the trim pieces) and telling the glass shop the nature of the installation. 
The windshield is held in place by a Urethane Adhesive, typically with a primer. NEVER install a windshield with RTV Sealant. The windshield is a structural member of the car and RTV is not strong enough for the purpose. 
Replacing the windshield requires removal and replacement of the forward outer door seals. These seals, and an adhesive pad for the mirror, are included with the kit. The seals are installed using common black weatherstrip adhesive. 
Replacing the windshield requires removing the three outer black trim pieces (items 1 and 13 in the illustration above).  These are secured in place with screws that are hidden behind the outer door seals. The screws on the side of the glass are often very difficult to remove, and can usually benefit from the use of a small hand impact Phillips screwdriver. The trim across the top is removed (after removing the screws) by lifting the back straight up to clear the roof, and then toward the front of the car. Underneath the black trim is another stainless steel bracket, also held in place by screws. That should also be removed for the best results. When reinstalling the screws, be sure to put some RTV sealant on the screw threads as this is a common source of water leaks into the car. 
NOTE: NEVER use glue (aka "Rear View Mirror Adhesive") to install the mirror to the windshield. Due to the difference in thermal expansion between the mirror base and the glass, glue will actually cause the windshield to crack if parked in hot sun. 
CAUTION: With the windshield removed and the doors open, the roof may actually sag slightly. If the new windshield is glued in place and allowed to cure with the doors open, you'll find that the doors do not close well any more. To prevent this, it is extremely important that you close the doors as soon as the glass is set in place, and keep them closed for at least 12 hours. In cases where the windshield has been out for a long time, it may be necessary to lift up the front edge of the roof to get it back in alignment BEFORE gluing the windshield in place. Although there is a factory fixture available for this, you can do an acceptable job by lifting the center of the roof from the inside. You will need to remove at least the dome light, or the headliner, and the console, to get to surfaces that are hard enough to move the roof into position. This is NOT normally required on same-day replacements.
Written by James Espey, DeLorean Motor Company (Texas)

Updated March 2023