Aggregate productivity, fundamental cause of long-run economic growth, plays a crucial role in determining economic development and living standards of nations. The main source of aggregate productivity growth is technological advances that are the outcomes of firms' and entrepreneurs' innovative activity. Complementary to the growing literature that studies how firm dynamics shape technological change, my dissertation focuses on how financial decisions of these agents affect this process. The three chapters of my dissertation provide theoretical, empirical, and quantitative investigation of the interplay between financial and innovative actions of heterogeneous firms along with its implications on aggregate productivity growth. Chapter one studies the impact of financial system on net firm entry, an important source of aggregate productivity growth. Selective funding of most promising ideas by financial intermediaries creates a trade-off between the mass of entrant firms and their average contribution to aggregate productivity. This chapter highlights the relevance of firm heterogeneity for the relationship between finance and growth, and discusses the theoretical and empirical implications of the resulting trade-off in firm entry. Chapter two also builds on the above mass-composition link, and uses it to study the permanent productivity losses due to sudden stops (SS). The model embeds the main mechanism into a real business cycle small open economy framework to measure the forgone productivity contribution of entrants deprived of funding. The theoretical prediction is that, during SS, smaller yet on average more productive cohorts enter the market. Chilean plant-level data that cover the 1998 SS verify this prediction, while the calibrated model demonstrates the quantitative significance of heterogeneity and selection in measuring the long-run productivity loss. Chapter three focuses on a specific financial intermediary that is especially relevant to innovation and growth, namely venture capital (VC) finance. It studies VC's quantitative impact on firm dynamics and economic growth using a new dynamic equilibrium model of technological change with heterogeneous firms and an explicit VC market. Distinctively, the model incorporates a unique feature of VC firms: their operational knowledge (OK) bundled with their investment. Experiments based on the estimated model highlight the quantitative relevance of OK and analyze policy implications.