Arguably, the most significant tire innovation was the vulcanization process. In 1843, Charles Goodyear figured out how to remove sulfur from rubber. He learned that if you did so and then heated it this would improve rubber’s ability to maintain its elasticity. The process had the further benefit of making rubber waterproof. Goodyear's process was patented in 1844.
In 1888, John Boyd Dunlop built upon Goodyear's innovation when he developed the first practical inflatable (pneumatic) tire for his son’s bicycle. Dunlop's idea was to use air pressure to reduce the shock transmitted from the road surface into the bicycle. Leveraging this innovation, Andre Michelin, in 1895 developed a pneumatic tire for automobiles.
However, his invention did not work very well.
Because of this, it wasn't until 1911 that the first practical inflatable automobile tire was invented. This was when Philip Strauss came up with the concept of using an inner tube to contain the air. Thus, Strauss developed the air-filled car tire, by combining a tire with an air-filled inner tube. Strauss marketed the tires through his company called the Hardman Tire & Rubber Company.
Interestingly, the first tubeless tire was developed and patented long before that.
In 1903, P.W. Litchfield, working for the Goodyear tire company, came up with a reliable tubeless tire. However, Litchfield’s tubeless Goodyear tire was not used until 1954, when it was finally fitted to a Packard model. And while there have been many incremental developments to improve tires since then, by and large they still operate based on Litchfield’s principle of the compressed-air inflated tubeless tire.
However, one tire innovation that has caused a great deal of both interest and controversy is the substitution of nitrogen for compressed air to inflate automotive tires.