The Transit of Venus might seem at first glance to be little more than an interesting diversion  however, it's played a vital part in the development of the history of astronomy, and has been right at the heart of the development of science, as our timeline shows. Indeed, as you can see here, study of transits of other stars is integral to the development of major theories in astrophysics and cosmology, as well as the search for the AU.
c250 BC Solar System Geometry 
Eratosthenes estimates the radius of the Earth

130 BC  
Early star catalogues
Astronomy as a science cannot get started without star catalogues, and the first ones were produced a very long time ago and were remarkably accurate and reliable. (There were no lenses, and so no telescopes, but they used extremely long sighting lines). Two particularly dedicated early astronomers are Hipparchus (Greece , c.130 B.C.)  hence the HIPPARCOS satellite  and Ulugh Begh (Samarkand c. 1400, murdered because his colleagues were afraid of his knowledge). 
Before 1600 Solar System Geometry 
Guesses of the distance to the Sun

Late 1500s Solar System Geometry 
Brahe
Tycho Brahe (1546 1601), son of a Danish nobleman, was so struck as a child by an eclipse which occurred at the predicted time that he pledged his life to astronomy, and his family's wealth supported his work. He contributed to many areas of astronomy but there are two for which he is especially remembered. In 1572 he saw, and recognised the significance of, a bright new star, now known as Tycho's supernova. He also plotted the tracks of the planets with unprecedented care and passed the results on to one of his students, Johannes Kepler. The tracks are very complicated as seen from the moving platform of the Earth, but thanks to the accuracy of the data, Kepler was able to extract underlying simple rules of planetary behaviour, which Newton was able to explain through his even more fundamental laws of motion and gravity. 
c.1610 Astrophysics 
Kepler discovers the rules of planetary motion
Johannes Kepler assembled many years of planetary measurements, especially from Brahe, and found purely empirically (ie not deduced from an underlying theory) that they obey 3 simple rules, of which the one we need here is that planetary distances are proportional to the 2/3 power of their orbital period (their "year"). Or in symbols: T^{2} is proportional to R^{3}. The underlying laws are those of Newton, written in absolute terms but involving one of the six universal constants (see The Gravitational Constant). So measuring the planetary "years"  easy for the closer ones if not for the very distant ones  gives all the RATIOS of all distances. That is why it was so essential to measure one distance in absolute terms. We can then, quite literally, relate everything right back to the length of Eratosthenes' stride. 
1660 Astrophysics 
Newton's theories of dynamics and gravity
Newton greatly clarified the ideas of earlier scientists such as Galileo, and set them in mathematical form so that they had predictive power. He then created a theory of gravity and tested it on the Moon. In the process, Kepler's rules for the planetary orbits appeared as straightforward consequences of the laws. So his work is the mathematical structure behind all orbital analysis until the mid 20th century, when Einstein's general relativity cleared up some anomalies left by Newtonian analysis, and in its turn made predictions for extreme conditions such as neutron stars, for which Newton 's Laws fail to be even approximate. 
1676 Solar System Geometry 
Romer measures the speed of light
It's not hard to show the speed of light is very high (e.g. you and a friend with a horse; both have a lantern and a hat to put in front of it to make a signal  you can imagine the rest). But how fast? Infinitely fast? Ole Romer in 1676 used the satellites of Jupiter in much the same way as the lantern, with Jupiter as the hat. He discovered the timings of the satellite eclipses or transits changed as Jupiter came closer to us (or moved away), in our different orbits. He got 225,000 km/sec  30% too low, but showing clearly that it was not infinite. 
1680 Solar System Geometry 
Halley suggests using Venus' Transits to measure the Astronomical Unit
If we can triangulate any solar system body it gives the scale to the whole Solar System thanks to Kepler's Laws. So we want to choose the body closest to us which is orbiting the Sun, to give the best chance of getting a measurement. The candidates are Mars, any asteroid which comes within the orbit of Mars, and Venus. The crucial point is that it needs something as a backdrop against which to measure the chosen body. A frequent opportunity is given by watching Mars occult, or nearly occult, any distant star. Venus is inside Earth's orbit and so offers a special but rare opportunity when it passes between us and the Sun. The Sun itself provides the backdrop. We can then measure the distance of Venus and deduce the distance of the Sun. When it became possible to measure the distance of passing asteroids directly by timing radar pulses, measuring the AU was a solved problem. It was Halley who suggested Venus would be perfect for this; Delisle suggested a similar, but distinct, method. 
1728 Solar System Geometry 
Bradley discovers stellar aberration
Since light does not travel infinitely fast, the direction in which we perceive a given star is changed slightly by the speed of the Earth in its orbit  the effect will be in the opposite sense in six months from now when the Earth will be on the opposite side of the orbit. This was an amazingly clever idea for 1728 when it was measured by Bradley. All stars show this to the same extent, it is not related to the distance of the star. The aberration angle gives the speed  it was the first measurement of the speed of the Earth. Since we know the duration of a year this gives us the circumference and hence the radius of the Earth's orbit. In effect this upstaged transits as a method of measuring the AU, but these were new ideas and they had to be tested. 
1776 Astrophysics 
Maskelyne weighs the Earth
Once you know G here, it is assumed that you know it everywhere in the Universe. Maskelyne measured it in Scotland, in fact, in 1776. A mountain pulls a pendulum sideways and the Earth pulls it downwards.

1810 Stellar Geometry 
Bessel discovers the parallax of a distant star
The next step was to discover the distance of nearby stars in the night sky. The diameter of the Earth is far too short to hope to triangulate the distance to the stars. But the diameter of the Earth's orbit  by this stage known well enough to be used  provides a much longer baseline. Fortunately there is an abundance of very distant stars to provide an almost fixed backdrop. Bessel was the first person to achieve a successful measurement, of 61 Cygni (0.3 arc sec). Before that noone really had any idea how far away the stars are. Measuring stellar distances is called astrometry. 
1871 Astrophysics 
The thickening plot of aberration

19th century Solar System Geometry 
Transits of Venus

1901 Solar System Geometry 
Eros geometrical measure

1905  1913 Cosmology 
Einstein's theories of relativity

1926 Astrophysics 
Eddington makes the sun shine
There was no good reason known for the stars to shine, and to shine for so long, before Eddington (1926) calculated the balance between gravity holding stars together and nuclear energy tending to blow them apart. Huge amounts of subsequent computation have led to sufficient understanding of stars to know how luminous different types of stars must be. By recognising types of stars in other galaxies, galactic distances can be found. This in turn determines the age and size of the whole observable universe. Successive links have taken us from a walk to Alexandria to an imaginary journey to the limits of the universe! The temperature of the early universe can be found by the helium produced in thermonuclear reactions, so we know directly and for sure that it was very hot. The idea of a Big Bang is not so direct, it involves a lot more assumptions. 
1930s Cosmology 
Movement and structure of galaxies

1932 Astrophysics 
The discovery of Neutron Stars

1950s Cosmology 
Big Bang cosmology In his 1950 BBC radio series, The Nature of the Universe, Fred Hoyle mockingly called this idea the "big bang" considering it preposterous. Yet the theory  and the derisive term  have become mainstream, not only in astronomy but in society as well.

1989 Stellar Geometry 
Hipparcos spacecraft measures a million stars

1990 Stellar Geometry 
Doppler wobbles reveal other planetary systems

1996 Solar System Geometry 
Official definition of the AU
What is the Astronomical Unit?

2004 Stellar Geometry 
SuperWASP
SuperWasp is an array of specialised digital cameras with the ability to capture data about an enormous numbers of stars. Using this information it is possible to detect planets around other stars. 
2015 Stellar Geometry 
Darwin space telescopes search for extrasolar planets
