For a couple of hundred years the sun-centered (heliocentric) theory of the solar system has guided astronomical discovery.  Even today, when an astronomer observes the movement of a planet in our solar system, or a distant one, the sun-centered model guides the astronomer in formulating hypotheses to test.

Scientists use theories to guide them in forming hypotheses by using the following steps. 
Theory: "If the sun is the center of the solar system..." 
Observation: "and the periodic movements of Mars in the sky are faster than earth..." 
Hypothesis: "then Mars must be closer to the sun than earth." 

The next step involves experimentation and further observation to prove or disprove the hypothesis. 

Introns and exons.  Biology's central theory of evolution help us to understand why the coding sequences of genes (exons)  are always broken up with what appears to be gibberish sequences (introns). 

Tumor growth:  "Tumor's, like populations of rabbits, are prone to rapid and strong evolutionary pressures.  Just as the offspring of the fastest breeding rabbits soon dominate a rabbit warren, so the fastest dividing cells in each tumor come to dominate at the expense of more stable cells.  Just as mutant rabbits that burrow underground to escape buzzards soon come to dominate at the expense of rabbits that sit in the open, so mutations in tumour-suppressor genes that enable cells to escape suppression soon come to dominate at the expense of other mutations.  The environment of the tumor is literally selecting for mutations in such genes as the external environment selects rabbits.  It is not mysterious that mutations eventually show up in so many cases.  Mutation is random, but selection is not."  Matt Ridley, "Genome," pg. 236-237. 

The Red Queen Hypothesis:  In Alice in Wonderland there is a scene where Alice and the Red Queen must run as fast as they can to get nowhere because the world is running by at the same speed.  Van Valen used this as a metaphor to illuminate biotic evolution.  In a predator-prey relationship, or a host-parasite,  or a plant-herbivore, or a disease-host relationship, any evolutionary adjustment made by one species tends to be matched by related genetic changes in the other.  The faster the antelope species becomes over successive generations, then the faster the lions become. 

• plant alkaloids and herbivore enzymes
• insect and insect galls
• HIV and the human immune system.  This relationship (a disease-host) is different than the others because the disease organism, in this case a virus, reproduces (run's in the metaphor) much faster than its human host.  The faster an organism produces new generations the faster that organism evolves.  The virus reproduces new generations in minutes or hours, the human host takes 20 years.  Thus the HIV "out runs" the ability of our immune system to keep up in what is often described as an ever escalating "arms race."

 

• Compare the awkward and hard to control fore "fin" of the whale, as it flops around when the whale breaches, with the pectoral fins of a tuna fish, and you see that evolution has a long way to go to completely adapt its' ancestral arm as a swimming fin.
• The human eye resulted from the invagination of light sensitive spots first seen on the surface of translucent vertebrate worms.  The evolutionary sequence leading to the mammalian eye results in the light entering the eye having to pass through a layer of tissue full of nerves and blood vessels in order to hit the retina.
• The thin veils of tissue that suspend mammals intestines and other abdominal organs hangs from the back bone.  When human primates adopted the upright stance they were stuck with this ancestral legacy which causes common problems such as tears and digestive problems.  If you were designing an upright animal from scratch you would hang the mesentery from the ribs, not the back bone.  Some human back, hip and knee problems have the same ontogeny.