How does Samsung's "quick charge" work? How do the batteries work?

Will those batteries have a shorter lifespan? Will the "quick charge quality" get worse over a period of time? And why aren't there other companies using this technology?
As seen on Android Police

You've probably heard of quick charging, turbo charging, adaptive fast charging, rapid charging, and Qualcomm Quick Charge 2.0 before - or at least one or two of these things. What you may not know is that all of them are actually basically the same thing, based on the same licensed technology from Qualcomm known as Quick Charge.

How does Quick Charge work?
How do the batteries work? Will they have a shorter life span?
Will the Quick Charge quality get worse over a period of time?
It's already explained in depth by @beeshyams. It basically works by drawing more power, safely.

To summarise, normal charging is done at 0.5 to 0.8 C (C is charge rate) and fast charging done at 1 to 3 C. Please note that the exact or indicative charging rate is not revealed in any OEM documentation despite extensive search and it is unlikely that OEMs will reveal such details, deeming it &quot;proprietary&quot;

It affects the battery in two ways:

A common feature while using fast chargers is raise in temperature of battery (since more current is being pumped in and power (read heat) is proportional to square of current) and this is inimical to good health of battery, which is extensively  covered here.

Short Term (Battery capacity after charging) Battery is not really fully charged as it does not undergo charging spending enough time in all stages, compared to conventional charging. In simple words battery may deliver typically 85% of performance compared to regular charging. Details on this are available here
Long Term (Battery life span) Battery life is specified in Cycles or discharge cycles. OEMs/ Battery resellers may specify this number, for example, it is 550 Cycles for Samsung Note 2

Quoting from BU-501: Basics About Discharging

Why aren't there companies using this technology?
There are several smartphone OEMs including ASUS, BlackBerry, Fujitsu, Samsung, HTC, Panasonic, Motorola that borrows this technology from Qualcomm.
What about Apple?
Here's a list of features Apple left out even in their latest iPhone 6S. They don't support Quick Charge yet.
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See also:
Qualcomm Quick Charge FAQ
,
Samsung Fast Charge FAQ