The first hand-held calculators were released in 1970 by Sharp and Canon, and they weighed around 1.7 lb.  The pocket calculators, however, were released by Bowmar in 1971 and it had the four functions (subraction, addition, multiplication, and division) and an eight-digit red LED display.  It went on sale for $240.
Hewlett Packard then came out with the first scientific function calculator in 1972 (the HP-35) and that invention was then followed by engineering calculators, programmable calculators, alpha-numeric calculators, and expandable (with RAMs, ROMs, etc) calculators.  Though HP seemed to come out with all the new and better calculators, Texas Instruments diligently came out with its own scientific calculators (with the same functions) in different designs.
The pocket calculator has now become an everyday, taken-for-granted presence.  It is, to define it, a small (relatively, compared to its predecessors) battery-powered or solar powered electronic digital computer that is made with integrated circuits and semiconductor technology.  Simpler ones are limited to 8-10 digits and they have singe-number displays and have limited mathematic functions that are available—they differ from the scientific calculators, which are more like general-purpose computers (with many, many mathematical functions available for the user).

*Pictures from http://www.etedeschi.ndirect.co.uk/bowmar.jpg and http://en2.wikipedia.org/upload/6/66/TI85_graphing_calculator.jpg, respectively

Sources:
Ball, Guy. The History of Pocket Electronic Calculators. 12 Oct 2003. <http://www.geocities.com/SiliconValley/Park/7227/timeline.html>

Tedeschi, Enrico. Bowmar. 12 Oct 2003. <http://www.etedeschi.ndirect.co.uk/bowmar.jpg>

Wikipedia. Calculator. 12 Oct 2003. <http://en2.wikipedia.org/wiki/Calculator>

Wikipedia. TI85 Graphing Calculator. 12 Oct 2003. <http://en2.wikipedia.org/upload/6/66/TI85_graphing_calculator.jpg>

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