From Lostpedia

My theory, updated:

Alvar Hanso and Jacob are twins, grandsons to Magnus Hanso who was the captain of the Black Rock, which crashed on the island in the 19th century. Being his descendents, they were born on the island and therefore know many of the island's secrets.

"Jacob feels the same way about technology as you do" (Ben Linus to Locke in The Man Behind the Curtain)

A rift grew between the brothers as Jacob wants to leave the island alone while Alvar wants to use the island's special properties to help save humanity from destruction. Alvar created the Hanso Foundation and joined forces with Enzo Valenzetti after learning of the Valenzetti Equation while Jacob leads the "Hostiles" - descendents of people who have found their way to the island - to try and stop him from exploiting the island's innate abilities.

The Incident, however it was caused, turned Jacob and some of his followers into a sort of collective living ghost, able to read minds and change into various forms but is commonly seen as the black smoke. It is similar to what happened to Desmond after the implosion of the Swan Station.

In an effort to study and discover more about the survivors to learn if they are a threat to his goals, some of the other forms it has taken include Christian Shepard, Kate's horse, Dave, Emily Linus, Yemi, among others.

"I looked into the eye of the island, and it was beautiful." (Locke)

In the form of the monster, Jacob kills the survivors and the Others he feels are a threat to his agenda. When encountering Locke in the jungle he attempted to pull him down a hole to bring Locke to him; he was not trying to kill him.

The island's healing properties are stronger for people born on the island than those who come to the island. This explains why Ben has aged from an early teenager to a 40 year old man while Richard Alpert has apparently aged very slowly in the same period of time, and why there are rumors that Alvar Hanso is well over 100 years old. It also affects people leaving the island, which is why Walt left the island as a child and returned weeks later but seemingly years older.

"It has not erupted in a very long time." (Olivia to her students in The Man Behind the Curtain)

The DHARMA Initiative, created by the DeGroots, who themselves are descendants of survivors of the Black Rock, came to the island to study its effects in the hope of utilizing its properties to help humanity. Among their many goals and experiments, they must find a way to keep the island's volcano from erupting and destroying the island.

Led by Ben, the Others - known as Hostiles to the DHARMA members - want to discover why women are dying when they become pregnant on the island. Richard Alpert is one liaison to the outside world, and he recruited Juliet to do research. Because several generations of Others have been born on the island beginning with the generation following Magnus Hanso, the problem of pregnant women dying probably began following the Incident, or it is the island getting revenge on the Others for their role in the Purge.

MISC IDEAS:

• Jacob can only be seen by a small group of people, consisting both of those he considers important (Ben, Locke) and by those with special abilities (Hurley, Walt, Miles).
• Naomi told the survivors the wreckage of flight 815 was discovered and there were no survivors. This is a cover up organized by the Hanso Foundation and employing Paik Heavy Industries for the purpose of taking public attention off locating the real wreckage. Naomi knows of the cover up and this is why she questions Matthew Abaddon about survivors as he instructs her on the mission to the island.
• Ben spends much of his time off the island. It was during this time that the cancer appeared. Had he not come back to the island when he did, it would have killed him.
• The island has strange time-warp abilities. For people born on the island, they age incredibly slow. For people who come to the island, they age slower than normal, and when people leave the island, they age more rapidly than they normally would have. This will explain why Walt will look much older than he should (years older, rather than months) when he returns to the island.