Classical growth theory
Classical growth theory connects population growth to the growth of labor productivity. This is a very basic view of economies, believing that productivity growth can expand a population to a finite point and beyond that point productivity will revert to a subsistence level. The implication is that physical resources are limited.
Neoclassical growth theory
Neoclassical growth theory believes that in the long run, physical capital per laborer and laborer productivity will not grow without increases in technology. In other words, physical capital can only drive so much growth and beyond a certain point, an economy will need new technology to continue to grow. The neoclassical theory also believes in convergence of economies: output per worker (or per-capita GDP) will become equal across countries, if all countries have access to the same technology and their financial markets are integrated
New growth theory
New growth theory is rooted in the notions that educating laborers (also referred to as investing in human capital) and providing incentives for laborers to discover new technologies are needed to drive continuous economic growth.