Early skis were wood and fairly straight with 4 mm sidecut (narrower at the waist than the shoulder and tail) with a little camber (ski bow up underfoot).
Ski construction has become very sophisticated over the last 40 years with everything from honeycomb cores to Piezo-ceramics that can convert high frequency mechanical energy to electrical energy.

Contents: Sidecut-Shape | Camber-Rocker | Materials-Construction | Books - Links

Sidecut - Shape:

The Kastle slalom used by 1964 medalists Pepi Stiegler, Billy Kidd and Jimmie Heuga had a 6.75 mm sidecut on a 64mm waist.
The 1967 head 360 and slalom were 86.1 - 71.5 - 81.0 mm [shoulder - waist - tail width] with a 6 mm sidecut.

In 1974 head pioneered the concept of a short (180 cm), wide (92.5-71.5-80) ski with more (by standards back then) sidecut (7.3 mm), with the Yahoo. It had a foam core wrapped with fiberglass. It was more for hot dog skiers than racers. I still have my Yahoo 2's and ski them with tele bindings.

In the late 70's and early '80's the Mahre brothers were winning on K2's with a 7 mm sidecut and Ingemar Stenmark used an Elan with 8 mm sidecut, but they were still relatively long (205 cm) skis.
In 1974 snowboards were introduced with a 17 mm sidecut.
In 1990, the aluminum K2 GS Race, had a 10mm sidecut. By '93, Dynastar had a 12mm cruiser, the G9 race ski. K2 revised the Velocity as the MSL, which in its second year featured a 12mm sidecut.

In 1992 Kneissl came out with the 180cm Ergo at 100-62-100mm - 19mm of sidecut with a radius of 14 meters.

In 1993 Elan introduced "Sidecut Extreme", or "SCX" skis, termed parabolic skis. Their 203cm mold for a GS race ski with a 110-63-105mm profile - that's a 22.25mm sidecut with a radius of just 15 meters

In 1994 the K2 Four had a 14 mm sidecut describing a 22 meter radius at the 195cm length. Bode Miller popularized them and shorter larger sidecut skis in general when he started winning FIS races in NH with them in 1995.

The disadvantage to a pronounced sidecut is that the ski will be less stable at high speeds, preferring short, quick turns. Also, skis with a drastic sidecut will perform poorly in moguls.

In July 2011 the FIS (International Ski Federation) announced new limits on GS ski minimum length and turning radius to make them safer.
From 185 cm and 27 m to 195 cm and 35 m for GS.
Ted Ligety, GS champion, was skiing on 191 centimeter skis with a 28 to 29-meter radius area for shape.

About 80 percent of all World Cup racers signed a petition to protest against the changes.

The whole idea is to make it easier to carve a turn without scraping off speed by skidding.

Sidecut Length Turn radius
   4.2 mm         83 m
   7.3 mm 180 cm  35 m
    8 mm  205 cm  41 m
   14 mm  195 cm  22 m
   22 mm  203 cm  15 m
   19 mm  180 cm  14 m
   
Graph of bend radius (Calculated by the Howe method) - for eight different skis. Each ski is made with a different fixed sidecut radius (R11, R15 ... R33).

Longer skis of GS cut are seen to be more responsive (That is change in bend radius resulting from a given change in inclination angle). This can be seen by the slope of the curve for each ski.
An edge angle (on the snow) of 60 degrees (cosine = .5) creates a theoretical carving radius of one half the ski's sidecut radius. 75 degrees (cosine = .26) nearly cuts the theoretical carving radius in half again--about one quarter of the ski's sidecut radius
When the ski bends into a tighter radius arc than the turn the skier is trying to make, it will not carve--or hold--nearly as well as when tipped to the optimal angle.

   
Ted Ligety (2008-): 5 World Cup GS titles - Hermann Maier (1998-2004): 4 overall, 5 super-G, 4 GS titles.
Bode Miller (2003-2008): 2 overall WC championships, 2 super-G, 3 combined

Ski Size Chart & Buyer's Guide | evo, 2015
Turning radius Turn type Type of skiing, intermediate all-mountain
< 16m short carving
17-22m medium all-mountain, park & pipe
> 22m long powder, big-mountain


Rocker - Camber:

See: ELAN SKIS | Profiles


Materials:
You can write a book on ski design. This is a very cursory overview.

Skis were originally made of wood; Hickory and ash were most popular.
In the 1960's head popularized "metal" skis, a plywood core with an aluminum outer skin.
The disadvantage of wood was poor torsion strength due to its fibrous nature.

In the early '70's skis came out with foam cores wrapped in fiberglass.

Carbon fiber and aramid (Kevlar and Nomex) became popular later.

Modern skis can be classified into three different types. In laminated skis, various layers sandwich the core on top and bottom. In torsion-box ski construction, the layers wrap around the core. In single-shell construction, polyurethane foam is sometimes injected into the ski shell. As this foam expands and hardens, the top and sides form one sheet.
Read more: How ski is made - | MadeHow.com

At "Materials in Ski Design & Development" - TMS Hugh Casey says,
"The conflicting requirements (flexibility versus stability) are addressed by combining dissimilar materials with different functions within the structure, and in some instances employing multifunctional materials to enhance both the efficiency and the performance. The resistance to flexure becomes progressively higher (with amplitude) as the load is transferred to the higher modulus materials in the composite structure. Vibration damping is accomplished with rubberlike absorbing materials in the sandwich layers or in the core. Recent innovations have favored external damping devices, including mechanical and electro-mechanical devices such as piezoceramic materials. Piezo-ceramics can convert high frequency mechanical energy to electrical energy, and are employed to dissipate vibration motion through electrical shunts. Active damping with piezo-electric devices is under development for aircraft and automotive structures, but their use in non-critical structure, e.g. skis, is an interesting benchmark on the 'progress' in ski design and manufacture"

In 2012 there were 5 kinds of cores for skis: Plastic, Foam, Wood and Wood with Titanium. See:
Ski Construction Summarized
Ski Construction Explained: How Do Materials & Manufacturing Affect Performance? | Backcountry.com
The effects of core material and thickness on the performance and behaviour of a ski | Philippe Mastrogiuseppe - McGill University


Books:
Skiing Mechanics: John Howe: Amazon.com, 1983

Links:
Ski Technology - SnowAndRock.com
Skis - Ski Equipment - Mechanics of Skiing
Rocker Explained | evo outlet
Ski geometry - Wikipedia
Evolution of Ski Shape | International Skiing History Association
Relationship of carved turn radius and ski sidecut radius
Physics Of Skiing

last updated 1 Dec 2015