Models of economic growth aim to explain changes in aggregate output per capita using a heavily simplified version of the macroeconomy. Technological progress is the key ingredient in most growth models, and it is different assumptions about the role of technology in production and the development of technology itself that give rise to the variation in growth models.
Neoclassical Growth Models
The main neoclassical model is the Solow_Growth_Model, in which exogenous technological progress (technology is like 'manna from heaven') is the driver in the growth of output per capita.
'Augmented' Solow models such as Human_Capital_Growth_Models also include human capital as an input to production. Again exogenous technological progress drives economic growth, but qualitatively the results of these models fit the empirical evidence better than the standard Solow model.
The Ramsey_Cass_Koopmans_Model is also an extension of Solow, including a representative consumer who makes the optimal leisure/consumption trade-off. This allows welfare concerns to be analysed, and for the savings rate and interest rate to be endogenized.
Endogenous Growth Models
Endogenous_Growth_Models give a micro-founded explanation for technological progress. A common feature is the presence of externalities to knowledge creation, and how these are parameterised affects the growth results of the models.