In the re-imagined series, Cylon Basestars (also referred to as "baseships" or "Cylon battlestars") are by far the most prominent example of Cylon presence in the known universe. They easily dwarf a colonial battlestar and appear to be technologically superior in every way, including being able to release wings of hundreds of Cylon Raiders at the same time (according to the number of launch "slots" on the Basestar, it can release 792 Raiders).
Beyond this, not much is known. Basestar operations would suggest that they have large crew complements, although there is ample evidence to suggest their operations are largely automated. Indeed, the large complement of raiders would suggest on-board manufacturing facilities (The BSG Bible).
Its weapons complement indicates missiles on a similar principle to the United States' VLS system, which is capable of launching coventional or nuclear missiles.
Soon after the planet Kobol was discovered by the Galactica, a Basestar Jumped into orbit, resulting in the destrucion of 2 Raptors. Subsequently, Commander Adama devised a plan to destroy the Basestar by using a Raptor fitted with a Cylon transponder to sneak a nuclear warhead inside it. The Galactica-copy of Lt. Sharon "Boomer" Valerii flew a Raptor along with ECO Racetrack to infiltrate the inside of the Cylon Basestar. While inside, they saw that basestars have a vast, cavernous interior made of bio-mechanical components. There is also not distinct floor. The walls appear fleshy and alive, similar to the synthetic organs filling the interior of a Raider. Although they planned to fire off the nuclear warhead and then leave, the firing sequence jammed and Boomer landed the Raptor to exit it and deploy the nuke manually. Boomer was then surprised by a small army of naked copies of Boomer-copies of Cylon. They told Sharon that they loved her, and that she could not escape her destiny. Galactica-Boomer then activated the nukes' timer and ran back to the Raptor. Soon after their escape, the nuclear warhead detonated and succesfully destroyed the Basestar. This was perhaps the first time since the Cylon Attack's beginning that Colonial forces successfully destroyed a Cylon Basestar.
However, this encounter probably activated Cylon sleeper-programming in Galactica-Boomer, because when she returned to Galactica she shot Commander Adama in an attempted assasination ("Kobol's Last Gleaming, Part II").
Galactica-Boomer was later killed, so Lt. Margaret "Racetrack" Edmondson is now the only living member of the Galactica's crew that has ever seen the inside of a Basestar ("Resistance").