The most important contribution was probably the work by Robert Solow. In the 1950s he developed a relatively simple growth model, which fit the data on US economic growth remarkably well.
A common prediction of neoclassical growth models is that an economy will always move towards a steady state (or "balanced growth path"). In this steady state the growth rate of the economy depends only on the rate of technological progress. Policy measures like tax cuts or investment subsidies are believed to have no effect on this long-run growth rate.
Neoclassical growth theory boils down to saying that long run economic growth comes from technological progress. The next step is then to ask "Where does technological progress come from?", and this question has led to the development of endogenous growth theory.