This article contains one or more spoilers. This is a potentially bad thing. Be careful reading on if you are not well-versed in the continuum or not caught up!
Genesis of the Daleks
In Davros's first appearance, he is a member of the Kaled Scientific Elite, in charge of directing the war between the Kaleds and the Thals, another sapient species native to the same planet. In a significant retcon from the First Doctor stories that introduced the Dalek species, Davros creates the first Daleks on his own by mutating Kaled genetic material and placing the resultant entity in a Mark III Travel Machine.
The Fourth Doctor, who had gone back in time in an attempt to stop the Daleks from ever being created, unwittingly gave Davros the name for his creations, and the first Dalek was presented to the rest of the Kaled leaders hours later.
However, since they had been programmed to destroy all that was not pure Dalek, the first generation of Daleks turned on Davros, and appeared to have killed him. However, Davros was able to place himself in suspended animation, which enabled him to regenerate the damage that his creations had inflicted on him.
Destiny of the Daleks
By the time the Daleks became aware that they had not succeeded in killing Davros, they had built enough of themselves and wreaked enough destruction to become a feared power in the galaxy. They found Davros's body in the remains of his bunker on Skaro, and revived the scientist, planning to use his knowledge to put a quick end to their war with a race of androids called the Movellans. When Davros's first plan failed, he was captured by the Doctor, who placed him in a cryogenic prison.
Resurrection of the Daleks
The war between the Daleks and their mechanical opponents escalated when the Movellans released a virus targeted to destroy Dalek tissue. Davros was freed from imprisonment again, since he was the only remaining being with enough knowledge of the Daleks' physical forms to help combat the contagion. Unbeknownst to the Daleks, their estranged creator began experimenting on those presented to him to find a way to bring them under his control. When he was found out, Davros released the Movellan virus throughout the ship he was held in to destroy the Daleks the Supreme Dalek had ordered to kill him. However, since Daleks had been based on the Kaled genetic structure, Davros began to be affected as well, and he fled to heal himself.
Revelation of the Daleks
Davros managed to remove the contagion from his body before he was completely destroyed, but was reduced to only his head in the process. Undeterred, he installed himself as the leader of a stasis facility on a funerary planet, intending to use the bodies of those kept in the stasis tanks to build a new race of Daleks to seek revenge against the Supreme Dalek and the rest of the Dalek faction that had attempted to use him. The Sixth Doctor reveals Davros's true intent to the planet's inhabitants, which leads to a member of the stasis facility's staff bringing a group of the original Daleks to the planet. These Daleks fight their way past some of the new breed of Daleks, capture Davros, and take him back to Skaro, treating him as a high criminal.
Remembrance of the Daleks
Throughout an unknown period of time, Davros not only avoided execution by his creations, but perfected his new breed of Daleks, which he called the Imperial Daleks. Davros, as the Dalek Emperor of the newborn faction, waged war against the Dalek Supreme. He had managed to regenerate parts of his body, but was still incomplete, and stored his partial body in a customized Dalek Travel Machine that could open and close to reveal his head. The Dalek Emperor shell began to overwrite Davros's mind with that of a more traditional Dalek leader, and his two personalities were battling for control by the time the Doctor next encountered him.
The Imperial Daleks warred against the original Daleks, which Davros now called the Renegade Daleks for the acts aganst him that he saw as rebellion. After a lengthy conflict, each faction planned to use Time Lord technology to destroy the other. Davros's plan involved using the Hand of Omega, a relic of the first Time Lords, to transform Skaro's sun into a power source for time travel, and exploiting the subsequent control over time-space to destroy his opponents on all fronts. However, the Seventh Doctor had reprogrammed the Hand, and when Davros used it, it instead caused Skaro's sun to explode, devastating the planet.
The Stolen Earth/Journey's End
Davros played an unknown role for the Dalek side in the Last Great Time War, and was believed dead by the Time Lord faction when his ship was destroyed by an entity called the Nightmare Child. However, a Dalek named Caan, the sole survivor of an elevated sect of Daleks known as the Cult of Skaro, travelled back in time to rescue Davros from the doomed ship and bring him out of the era of the Time War. Once out, Davros began to grow new Daleks using the cells of his body, and took enough of those cells from his chest to leave his lungs exposed.
The new horde of Davros-born Daleks hid one second out of sync with the universe so that they would be undetected while they snatched planets to arrange in a specific way around the Medusa Cascade, which allowed them to build a bomb with the potential to destroy the entire multiverse. Somehow, being one second out of sync with the rest of time would allow the Daleks to not only survive the destruction of all of reality, but allow them to re-enter the universe as its only remaining life forms. The Tenth Doctor teamed up with his current companion as well as a clone grown from his severed hand, both of which were at that point half-human and half-Time Lord, to stop the bomb from going off and return all of the planets to their rightful places in time-space. The Doctor's clone destroyed the Davros-born Daleks, collapsing Davros's ship in the process. The original Doctor offered to rescue Davros, but the maddened and defeated Kaled claimed that he would rather die, and may have done just that when the ship exploded a few minutes later.
Despite being horribly scarred, crippled and having one cybernetic eye mounted on his forehead, the appearance of Davros in Series Four of the revived Doctor Who made it impossible for him to escape badfic.