Modern economic theory tends to separate itself from classical economic theory by looking at more than just the source of production and the invisible hand theory. Modern economics also looks at items such as the role of demand, money supply, and its effect on growth or monetarism and free trade. In some ways, modern economic theory is a much more macroeconomic study that looks at vast swaths of a single economy. This does not mean that an individual labeled a classical economist does not favor these items; it simply means that economics changes through history, with the term modern economics coming after the period of classical economics. There is still a distinct relationship between these two schools of thought for economic theory.
Classical economics started by looking at the resources used in the production of goods and services. How various entities gathered these goods and used them were of great interest in the 16th century. The purpose of these studies was in effect to determine how an economy could best use resources in a given market. For example, economists would study if a central entity would be best at the allocation of these resources or if numerous individuals working in their own self-interests would be sufficient. So, much study on this topic left open the need for a review as in modern economic theory.
Keynesianism is perhaps the single greatest modern economic theory, with all its benefits and flaws. Keynes looked at the role of demand in a market and what happened when there was too much supply and not enough demand. Essentially, he thought the government should step in and grease the market skids in order to spur economic movement. This, in turn, would allow companies with the supply to remain profitable and continue on in their natural course of business. Employment, however, was not necessarily something Keynes took into account, since he could not answer whether or not full employment would occur in this scenario.
Money supply economics also comes from modern economic theory. Here, using a central bank to govern interest rates and the amount of money in a market is important. This theory is necessary to control inflation and manage growth in order to not exceed upper limits in the economy.
Open markets and free trade between countries is another modern economy theory tenet. In short, free trade is necessary for a country to have a thriving economic center. Most countries would desire an equal balance between imports and exports or a situation where imports are far below exports because this means more currency remains in the country. The ability to move goods between domestic and other international markets also allows for growth and expansion. Modern economic theory may have several different concepts on how this is best accomplished.