Although, in crushed vintages, much of the juice comes off as free-run, there is still a considerable amount of juice left in the pomace. This can be higher in bitter and astringent phenolics, but often has a higher level of flavour than the free-run, so a proportion can be blended back.
The important feature of pressing is to press gently, so as not to damage the solid portions of the vintage too much and so extract too much bitterness and astringency, but effectively, so that there is a good level of juice extraction (about 70% w/w).
Normally presses will run on several cycles with a crumbling of the pomace ‘cake’ in between each one. The gentleness but effectiveness of this crumbling often defines the press quality.

There are several different types of presses in use:

Vertical screw press (basket press)

Vintage is placed inside a (usually) cylindrical ‘basket’ made of wooden slats. Pressure is applied manually or hydraulically by a moving plate either at the top or the bottom of the press pressing the vintage against a stationary one at the opposite end.
Press filling and cake crumbling is slow and labour-intensive
High pressures are required, but pressing is slow
The juice is filtered by the pomace as it is extracted, so can be of good clarity.

Horizontal screw press (e.g. VASLIN)

The fruit is loaded into a similar basket as with a basket press, but through an opening at the side. There is a stationary screw thread running throughout the basket that changes direction in the middle. At either end of the basket are plates that slot into the inside of the basket. These move together (thus pressing the vintage) if the basket is turned in one direction and move apart (thus crumbling the cake) if the basket is turned in the opposite direction. There is usually a series of chains and hoops between the plates in order to assist in the crumbling of the marc.
The press cycle is much shorter, as filling, cake crumbling and emptying is very quick.
Medium pressures are used.
The crumbling can be a bit violent.

The pneumatic press (e.g. BUCHER, DIEMME, WILLMES)

The vintage is placed inside a perforated drum and, using compressed air (or water), pressed against the perforations by an inflatable bladder or a polypropylene membrane.
Press cycle is not much longer than with the horizontal screw press, particularly as these can be axially filled.
Low pressures are used and these are very controllable.
Crumbling is gentle
Generally regarded as producing the highest quality juice.

A variant of the pneumatic press is the tank press, where the vintage is placed into a non-perforated cylindrical tank and then pressed against internal drains with a membrane. The advantage with this system is that oxygen contact with the must can be significantly decrease, but, as the drainage surface is smaller, press cycles can be longer.

The continuous screw press

The vintage is introduced into a perforated drum with an Archimedes screw inside it. This pushes the marc towards a resistance at the far end, either a weighted door or a plug of pomace, so that the juice is expelled out of drum’s perforations.
A continuous process with the potential for a very high throughput
High pressures are used
Works OK if juices are fractionated as they leave the press, but can easily be misused.