This is a comparative review of business cycles and economic growth, according to the heterodox approaches, to improve the dialogue and the knowledge about it. Special attention is given to the endemic problem of the business cycles that modern economies suffer, such as successive and distorted periods of boom and bust, with great impact in the productive system and the social welfare and wellbeing. The article is based on the Austrian business cycle theory, linked with its theory of capital, and its development among the generations. Also this article offers an effort to build dialogue with other economic schools and approaches, including some mathematical support to connect the Austrian theory with the Chicago School and the new-institutional approach.