Alembic is not that well-known a company, unless you play bass or guitar. The company creates instruments tailored to the individual artist rather than players as a whole (though they do have production models, costing twice that of nearly any other, which are produced in much smaller numbers). Their instruments are works of art in themselves, not just tools of art. To put it bluntly, there's an argument to say a Les Paul Custom is nothing compared to a custom Alembic (although ultimately of course it's a matter of personal taste). They also create after-market pickups that are often as expensive as the instruments they are put in1.
Alembic was founded in 1969 by Ron Wickersham and Susan Frates (later Wickersham). They worked with The Grateful Dead (they actually moved their offices into the same building as the Dead) to help improve the quality of their records. At this time they developed their pickups and electronics; the final versions (low-impedance pickups and active electronics) were first installed in Phil Lesh's and Jack Casady's hollow-bodied basses. They also started doing modifications to help improve the physical (unamplified) sound of the instruments. They started making instruments in 1971, the first one being a bass (though it wasn't finished until 1972). In 1972 Stanley Clarke (probably the number one reason why Alembic is better known for basses rather than guitars) got his first Alembic bass. In 1976 they produced the first graphite neck-through-body instruments. Of course Stanley Clarke got one of the first ones, in case you were wondering. In 1980 they introduced the 'Activator' pickups, a line of modular pickups that allowed players to get an Alembic tone out of basically any instrument, without soldering and, in many cases, no body alterations.
Alembic have almost always had some sort of practicality in their body designs. For instance, the original body shape (the Standard Point) came to a point at the bottom so that you had to put it on a stand, or risk damage to a very expensive instrument. This was their solution to prevent breaking the instrument by cracking the neck (neck-through models are basically impossible to repair if the neck is damaged). Some of the other early styles were similar (in concept as well as top design), but were probably better able to balance against a wall (it's tough to say; not many people would probably try and find out). Later bodies had emphasis on a bit more traditional design, for better balance2. There are also those designs that come from customers, such as the Spyder3, the Tribute4 and the Further5.
The answer to the question what is customisable on an Alembic: your only limitations are your imagination, the size of your cheque book, the laws of physics, legal restrictions (For example, you can't get a Stratocaster headstock, as Fender has it trademarked), and your sense of self-control. In other words, everything is customisable if it's possible (necks need to be wide enough to have separation between the strings) and if you're willing to pay for it. Even budget models (£2,000 for a budget model?) are customisable; you have a choice (by that I mean a select few) of top laminates for no extra charge.
Ummm, What Does This Switch do Again?
Alembic does have great electronics. However, the nature of the electronics can make for some confusion or issues with switching mid-song. While this really isn't the case for most of the low-end models, the higher-end models (especially the Series IIs) generally have numerous switches that have all sorts of effects on the tone. Knowing your instrument becomes very important. Even with knowing your instrument, the Series II can still be a heck of a thing to try and change on the fly6.
Why Do Fretless Basses Have To Act The Way They Do?
Some of Alembic's fretboard inlays are, how to put this, freaking unnatural. To explain: while the standard ones are rather drab (if you would call mother of pearl or abalone drab), some of the more deluxe ones are quite literally works of art. This is not an issue for any sort of fretted instrument. On fretless basses, it does. The sound of the instrument is partly dependent on what the string is pressing against. On a guitar or bass (guitar) this is metal, on a fretless bass this is whatever material that the string passes over, meaning that the sound would change as it moves from wood to silver to abalone to... whatever, the point is, WHY? OH WHY *insert name of divine entity or not here* WHY?
Why Are They That Expensive?
One of the major reasons that they are so expensive is that nothing is mechanised. All the body shaping and all that (aside from the slots for frets7) is done by hand (okay so power tools are used, but that's still beside the point). They also operate out of a single factory in the US; they only manage to produce about 1,500 instruments a year. Necks are always made from several pieces of wood (lower end generally have walnut veneers, higher end have purplehart or ebony laminates, others have a custom laminate structure for aesthetic purposes). Most are through-body necks, and the set necks are much deeper (they go further into the body) than other guitars/basses. They all have a top wood (like the Gibson Les Paul), and many have a back wood. Most have a ebony fingerboard, something not seen often outside the orchestral theatre. They also have a habit of using cocobolo (an absolutely gorgeous tone wood, with a reddish or orangish brown colour and great contrast, if under bright lighting) as a top/back wood, which is quite expensive due to its protected status. It should also be mentioned that their instruments are highly desirable due to the clean tone that they offer.
More than just Instruments
Instruments are not all that Alembic makes. In addition to the aforementioned modular pickups, they also make preamps done to the same standards and principles of their instruments. They also make the 'Blaster', a modification that acts as an 'active/passive switch' allowing for an Alembic-like preamp to be used (and turned off if you wanted) on a instrument that is not Alembic-equipped. They also made custom PA systems; does anyone remember the Grateful Dead's Wall of Sound?