When I first started in the hobby wargaming meant playing with cardboard chits ("counters") on a hex-based map. If you wanted to use toy soldiers there were always lead-based miniatures, although they were usually fairly large scale and games tended to be played on the floor using rulers for measuring. Many used 54mm figures, or maybe 25mm. The most popular scale for ships was 1:1200. Being a miniatures gamer meant many hours of painting.
Over the years miniatures got smaller and tended to move onto tabletops (which helped as we got older) but recently the advent of inexpensive overseas labor has resulted in the age of the pre-painted miniature.
Most of these are used in ways that are more like board wargames than traditional ruler-based miniatures games. Some prominent examples include Axis & Allies Miniatures; Axis & Allies Naval Miniatures; Star Wars miniatures, HeroClix, Heroscape, Lord of the Rings Tradeable Miniatures Game; Wings of War, Battlefield Evolution and (soon) World Tank Museum.
At the same time there's also been an explosion of regular boardgames using "bits," such as BattleLore; Memoir'44; Nexus Ops; Tide of Iron, War of the Ring, etc.
My very first Milton Bradley "wargames" also had nice bits, back in the day, such as Broadside, Battle-cry, Dogfight and Hit The Beach, so we've almost come full circle. Still, the variety and quality of today's offerings have no precedents. It's a golden age for playing with toy soldiers.