I think that the theory of the invisible hand is very relevant in the 21st Century.
The globalized world is where goods are produced under a free market. Nations and their economies are geared towards a freedom of economic expansion. Adam Smith's philosophies of wealth accumulation and the free market are relevant now because more nations embrace it through liberal economic growth.
A significant part of capitalist theory is the invisible hand. Classical liberals, like Adam Smith, believe that the invisible hand is the mechanism through which all problems of the marketplace can be remedied. As Milton Friedman writes, the invisible hand represents "the possibility of cooperation without coercion." Thinkers like Smith and his followers like Friedman use the invisible hand to explain why external control of the marketplace is not needed. As a result of the invisible hand, government intervention is unnatural because the invisible hand can remedy any potential disruption. This allows the marketplace to operate in a free manner and represents freedom of choice. The invisible hand is an essential idea behind capitalism, free market entrepreneurship, and expansion of economic freedom.
[Adam Smith] made it clear in his writings that quite considerable structure was required in society before the invisible hand mechanism could work efficiently. For example, property rights must be strong, and there must be widespread adherence to moral norms,... (Helen Joyce, "Adam Smith and the invisible hand," plus.maths.org)
As the globalized economy embraces capitalism in the 21st Century, the invisible hand will become more relevant. Free market advocates will turn to it as a way to counter external control in the form of government intervention.