The stock exchanges are regarded as instrumental for mobilizing financial resources and for increased economic efficiency of investments by directing capital to investments with the highest returns. Empirical evidence suggests strong links between stock market indicators and growth particularly where there are high quality institutions. Tanzania is a low-income country with a nascent stock exchange. Basing on a review of literature and scanty data this article proposes major research and policy attention to include expansion of public knowledge, relation between the growth of the banking sector and stock market development, patterns of the microstructure elements per se and related stock exchange infrastructure (technology etc.), long-term relationship between stock market and economic growth, and investment in the supporting institutional and regulatory framework.