Before skiing was a sport, skis were in use by Scandinavian farmers, hunters and warriors through the middle ages. They were so integral to Scandinavian life that by the 18th century the Swedish army was training and competing on skis. The 19th century transition from using skis as a mode of transportation to using them as a form of recreation was not entirely unexpected, gaining in popularity and momentum as skis became first cambered allowing for a lighter, more manoeuvrable build of ski, and later made from hickory, a hard, tough wood that allowed skis to be made thinner and more flexible without scars and gouging to make the skis slower.
Antique Skis photo credit Vintage Winter640px
Antique Skis photo credit Vintage Winter
When Sondre Norheim demonstrated the Telemark ski in 1868, around fifteen years before the first skis were made from Hickory wood, he introduced the first skis with a sidecut narrowing the ski underfoot while the tip and tail remained wider for ease of turning. Norheim and his friends developed the first dynamic turns in downhill with the Telemark ski. As the 19th century pushed on, skiers began experimenting with layers of laminated wood, and at the turn of the century an Alpine unit of the French army begun the first series production of Telemark style skis.
It might surprise you to find out, however, that the first segmented steel edge wasn’t added to a pair of skis until 1928 when Rudolph Lettner who screwed steel segments into his skis to get better grip on hard snow. The skis worked well, but the edges tend to come loose, or break in two, which would end your ski day pretty promptly. At the same time, the first solid aluminium ski was prototyped in France. This began the experimentation with the use of different materials in skis. 
Vintage Skis photo credit Epic Ski640px
Vintage Skis photo credit Epic Ski
Advances in ski tech stalled between 1937 and 1944, when the first plastic bottom was made to go on Dynamic skis. The post war period, however, saw huge advancements in ski tech in a relatively short period of time. Manufacturers began to consider aluminium and plastic to ensure skis were more flexible and more durable, with aluminium bases less likely to be scratched or gouged with continued use. The 1947 Head prototype was a super lightweight aluminium sandwich ski, with a honeycomb core. The ski broke easily, has no edges to speak of and was too light to track well, but it formed a base from which future, successful Head skis were founded. When the Head standard ski came out in 1949, with its continuous full length steel edge, it became the most commercially successful metal ski of the time.  
When the first fibreglass reinforced plastic ski was brought out in 1952, it was a failure, as were a number of subsequent attempts. What they did do, however, was introduce the concept of a livelier ski that would be lighter and easier to turn than a metal ski. When the first polyethylene base was introduced in Austria in 1955, it introduced a material that didn’t need wax and could be fixed easily by melting more polyethylene into the gouges and scratches. The new polymer quickly supplanted the earlier plastic bases, like Cellulix. 
Vintage Skis 70s and 80s photo credit Out There640px
Vintage Skis 70s and 80s photo credit Out There
In 1959 the first successful plastic-fibreglass ski was invented in Montreal. 10 years later, the most popular compound for skis was fibreglass or aluminium/fibreglass, and in the next 20 years, the bulk of the steps forward in skiing were based on improving the plastic materials, making small steps in ski manufacture. During this time, sidecut was gradually creeding inwards from the 4mm introduced with the Telemark skis to between 7mm and 10mm, and after 30 years of stagnation in ski design, Elan and Kneissl introduced the deep-sidecut “shaped” skis. These new skis were heavily influenced by snowboard design, and they ushered in the advent of the modern age, where skis are built with differing camber, rocker and radius based on what kind of snow you are skiing. 
Modern Ski Shop photo credit Alp Sport640px
Modern Ski Shop photo credit Alp Sport