The Scientific Revolution that occurred during the Renaissance had major political and economic impacts in the long term.
In terms of economics, it led to more technology. The search for scientific knowledge helped lead to more experimentation with things that would eventually end up being useful for practical purposes. For example, we can argue that the printing press would not have been possible except for the spirit of experimentation that came along with this revolution.
Politically, the Scientific Revolution helped lead to the thought of the Enlightenment. Enlightenment thinkers tried to apply science and rationality to thinking about human society and politics. This led them, for example, to the idea that monarchy was an irrational form of government and that people ought to be able to govern themselves in more of a democratic form of government.
These impacts did not happen immediately, but they did come out of the Scientific Revolution.
It may not be an exaggeration to say that everything we have in our modern political and economic system is due to the Scientific Revolution.
From the foundation laid by great thinkers like Francis Bacon, Galileo Galilei, and Isaac Newton, we built the entire edifice of scientific knowledge. With the advent of empirical science, for the first time in human history we had a precise, reliable means of obtaining knowledge about the universe. There had been some advances in knowledge and technology before that point, but they took hundreds of years and were basically trial-and-error. The Scientific Method was a turning point, where human knowledge went from virtual stagnation to an exponential rate of growth.
The change was slow, even imperceptible at the time; but it is almost impossible to overstate the importance of this fundamental shift in human existence. Before science, we were little more than the savannah apes we had evolved from; after science, we are building robots that land on other planets.
All the sciences we now know were built from this foundation: Physics, chemistry, biology, and ultimately psychology, neuroscience, and even economics. The Scientific Revolution brought us industrial technology, then fossil fuel power, then electricity, and ultimately nuclear power, computers, and the Internet. All of this is an outgrowth of that basic Scientific Method first expounded by Francis Bacon.
With industrial technology and a more rational understanding of the universe came also new ways of political thought, and I do not believe it is an accident that modern democracy with universal suffrage and free-market capitalism both emerged in the 18th century, once the Scientific Revolution was in full swing. The concept of an industrial capitalist economy did not exist before that, and in ancient times Greece and Rome had "democracies" that were actually aristocracies. Industrialization brought the first sustained economic growth, the first true democracies, an end to slavery, and ultimately led to the high-tech information services economy we know today. Without the Scientific Revolution we would still live like Medieval serfs.
Scientific Revolution meant a period of great, important changes in science, philosophy and mathematics, literature, economy, politics. During this period of time, the role of church and religion was diminished, science taking the place of faith.
The new scientific methods replaced the human perception and observation alone and reasonable thinking replaced the superstitions and non-practical beliefs. New scientific fields of study such as astronomy, math, physics, came into universities' attention, while literature gained creativity and imagination.
The economic structure during Scientific Revolution was also changed and financial aid was meant to support the scientific development.
The following list emphasizes some important exponents of Scientific Revolution, such that: Galileo Galilei, who proved the inefficiency of Ptolemaic system, Johannes Kepler, who proved that the orbits of planets are elliptical, Isaac Newton, who proved the gravity, Rene Descartes, who replaced observation with deduction, Miguel de Cervantes Saavedra, who wrote Don Quixote, a great novel, where realism and idealism are brought together.