Hearts of Iron III uses the concept of “leadership points,” which represent intellectual talent. These points may be directed toward Research and Technology, among other things. Researchers do not work on an entire production model of a machine or unit at once. Instead, they research components of the final product, which will separately alter the combat values and other statistics of the final product. As you acquire new elements for each category of technology (say, a light tank gun or a light tank engine), you get closer to the point where you can produce a new model of equipment or implement a new warfare theory. Meanwhile, incremental improvements to existing units may result.
As your Technology improves, you will be able to build more advanced weapons or pieces of equipment, and you can replace (upgrade) the older equipment your armies are using in the field. Technologies you’ve selected to research are placed in a “research queue,” and they are researched in a sortable sequence according to how many leadership points you allocated toward research.
HOI 3 allows you to build a reserve of theoretical and practical knowledge as a result of either constructing units, or researching technology. These levels of theoretical or practical knowledge can also assist in your future technology research or production efficiency. Research creates theoretical knowledge, which helps with new and advanced concepts. Practical knowledge, on the other hand, is accumulated experience in working with and implementing technology.
If you’ve developed a technology, but you don’t build upon that knowledge, your level of knowledge will decay over time: scientists or engineers who are involved will move on to other things and factories will be re-tooled for other purposes.
For a cost, a country can negotiate with another country and agree to “license build” a unit type at the tech level of the other country. A license allows for the construction of a single brigade (or airwing, ship, etc.) at the other country’s tech level. You cannot license capital ships or nuclear bombs.