Shape memory alloy:
A shape-memory alloy is an alloy that "remembers" its original, cold-forged shape: returning the pre-deformed shape by heating. This material is a lightweight, solid-state alternative to conventional actuators such as hydraulic, pneumatic, and motor-based systems.
Shape-memory alloys have different shape-memory effects. Two common effects are one-way and two-way shape memory. A schematic of the effects is shown below.
One-way shape memory alloy
The One-way memory effect occurs when a shape-memory alloy is in its cold state, the metal can be bent or stretched and will hold those shapes until heated above the transition temperature. Upon heating, the shape changes to its original. When the metal cools again it will remain in the hot shape, until deformed again.
Two-way shape memory alloy

While the two-way memory effect is the effect that the material remembers two different shapes: one at low temperatures, and one at the high-temperature
Discovery history:
Shape memory effect was first documented in 1930s.while the basic phenomenon of the memory effect governed by the thermoelastic behavior of the martensite phase was widely reported a decade later by Kurdjumov and Khandros in 1949 and also by Chang and Read in 1951.

The nickel-titanium alloys were first developed in 1962–1963 by the United States Naval Ordnance Laboratory and commercialized under the trade name Nitinol (Nickel Titanium Naval Ordnance Laboratories). Their remarkable properties were discovered by accident by Dr. David S. Muzzey.
Properties:
Shape-memory alloys are considered to be engineering materials. These compositions can be manufactured to almost any shape and size. The yield strength of shape-memory alloys is lower than that of conventional steel.
But the high cost of the metal itself and the processing requirements make it difficult and expensive to implement SMAs into a design.
Applications:
i. Aircraft
  1. Developed the Variable Geometry Chevron using shape-memory alloy that reduces aircraft's engine noise.
  2. Adaptive wing that change the air foil for given angles of incident
ii. Automotive
iii. Robotics
iv. Medicine
v. Optometry
vi. Orthopedic surgery
vii. Dentistry
Illustrating Videos:
http://www.youtube.com/watch?v=fsBHF_j2FJ4
http://www.youtube.com/watch?feature=endscreen&NR=1&v=r-Bqse9cqo8
References:
http://www.stanford.edu/~richlin1/sma/sma.html
http://www.smaterial.com/SMA/sma.html