In the "War of Currents" era in the late 1880s, Nikola Tesla and Thomas Edison became adversaries due to Edison's promotion of direct current (DC) for electric power distribution over the more efficient alternating current (AC) advocated by Tesla.
During the initial years of electricity distribution, Edison's direct current was the standard for the United States and Edison was not disposed to lose all his patent royalties. From his work with rotary magnetic fields, Tesla devised the system for transmission of power over long distances. He partnered with George Westinghouse to commercialize this system. Westinghouse had previously bought the rights to Tesla's polyphase system patents and other patents for AC transformers.
Electric power transmission
The direct current electric power transmission system had many limitations that were recognized and solved by Tesla's alternating current. High loads of direct current melted copper wires and could rarely be transmitted for a distance of greater than a mile. Edison's response to this argument was to generate power close to where it was consumed and install more wires to handle the growing demand for electricity, but this solution proved to be impractical and unmanageable.
However, the single strongest argument against the DC system was that, because it maintained a constant voltage, it could not be stepped up or down with a simple transformer. This meant that separate electrical lines had to be installed in order to supply power to appliances that use different voltages, which led to an even greater number of wires to lay and maintain, wasting money and introducing unnecessary hazard. A number of deaths from the Great Blizzard of '88 were attributed to collapsing DC power lines that cluttered cities running DC power grids.
When Tesla introduced alternating current after filing seven patents for alternating current generators, transformers, motors, wires, and lights in November and December of 1887, it became clear that AC was the future of electric power distribution. Distance ceased to be a problem and high-voltage AC could carry the same amount of power that would normally melt wires using direct current. Most importantly, alternating current could be easily manipulated with a transformer to change voltage and current. A lamp needing five volts could draw power from the same source as a machine using twenty volts, unlike with the DC system. High voltage alternating current was sent from source to destination without melting wires and then stepped down to low voltages in homes and factories for local use.
Tesla's US390721 Patent for a "Dynamo Electric Machine"
AC vs. DC
The advantage of AC for distributing power over a distance is due to the fact that power is given by voltage × current (P = VI). For a given power, a low voltage requires a higher current and a higher voltage requires a lower current. However, since metal conducting wires have a certain resistance, some power will be wasted as heat in the wires. This power is given by P = I2R, or by P = V2/R (where V is the voltage drop along the wire, not the overall voltage). As such, low-voltage, high-current transmissions will suffer a much greater power loss than high-voltage, low-current ones, even though the overall transmitted power is the same. This holds whether DC or AC is used. However, it was very difficult to transform DC power to a high-voltage, low-current form efficiently, whereas with AC this can be done with a simple and efficient transformer. This was the key to the success of the AC system. Modern distribution grids often use AC in the 500,000 volt range.
This has begun to change in recent decades with the rise of DC bulk power transmission systems. The mercury arc valve and later power semiconductors such as silicon controlled rectifiers (SCRs) finally made it possible to build efficient, high power voltage converters using and producing either AC or DC. With this technology, high voltage DC power transmission can provide several advantages over AC, especially over very long distances or through undersea cables. However, since AC is the standard for power distribution to customers, the power from a DC transmission line is always converted back to AC.
Experts announced proposals to harness the Niagara Falls for generating electricity. Against General Electric and Edison's proposal, Tesla's AC system won the international Niagara Falls Commission contract. The commission was led by Lord Kelvin and backed by entrepreneurs such as J. P. Morgan, Lord Rothschild, and John Jacob Astor IV. Work began in 1893 on the Niagara Falls generation project and Tesla's technology was applied to generate electromagnetic energy from the falls.
Edison went on to carry out a campaign to discourage the use of alternating current. Edison personally presided over several executions of animals, primarily stray cats and dogs, to demonstrate to the press that his system of direct current was safer than that of alternating current. Edison's series of animal executions peaked with the electrocution of Topsy the Elephant. Edison opposed capital punishment, but his desire to disparage the superior system of alternating current ironically led to the invention of one of the world's most recognizable killing devices. However, it should be noted that it is the electric current that actually kills, and if Edison's voltages were high enough, his DC current would kill also. He was unable to make high enough DC voltages, however, because of the nature of direct current. Tesla could, using his transformer. Ohm's law states that if the voltage is high enough, the current through the body will also be high, because of the constant resistance of the body. Tesla's AC current does not kill if the frequency is high enough, it simply burns the skin without destroying the tissue as on lower frequencies. Eventually, the advantages of AC power transmission outweighed the disadvantages, and it was eventually adopted as the standard.
Edison (or reportedly, some of his employees) used AC to construct the first electric chair for the state of New York in order to promote the idea that alternating current was deadly. Popular myth has it that Edison invented the electric chair solely as a means of impressing the public that AC was more dangerous than DC, and would therefore be the logical choice for electrocutions. In fact, the chair was primarily invented by a few of his employees, in particular Harold P. Brown, working at Menlo Park. 
A horrible sidenote to make, the technicians on hand misjudged the voltage needed to kill the condemned prisoner, William Kemmler. The first jolt of electricity, delivered on August 6, 1890, was not enough to kill Kemmler, and left him only badly injured. The procedure had to be repeated and a reporter on hand described it as "an awful spectacle, far worse than hanging". George Westinghouse commented: "They would have done better using an axe."
The Falls to Buffalo
Some doubted that the system would generate enough electricity to power industry in Buffalo. Tesla was sure it would work, saying that Niagara Falls had the ability to power the entire eastern U.S. On November 16, 1896, the first transmission of electrical power between two cities was sent from Niagara Falls to industries in Buffalo from the first commercial two-phase power plants (known as hydroelectric generators) at the Edward Dean Adams Station . The hydroelectric generators were built by Westinghouse Electric Corporation from Tesla's AC system patent designs. Tesla's system designs alleviated the limitations of the previous DC methods. The nameplates on the generators bear Tesla's name. He also set the 60 hertz standard for North America. It took five years to complete the whole facility.
Edison's inventions using DC ultimately lost to AC devices proposed by others: primarily Tesla's polyphase systems, and also other contributors, such as Charles Proteus Steinmetz (of General Electric). With the financial backing of George Westinghouse, Tesla's AC replaced DC, enormously extending the range and improving the safety and efficiency of power distribution. Tesla's Niagara Falls system marked the end of Edison's roadmap for electrical transmission. Eventually, Edison's General Electric company converted to the AC system.
New York City's electric utility company, Consolidated Edison, continued to supply DC current to customers who had adopted it throught the twentieth century. In January, 2005, Consolidated Edison announced that it would cut off DC service to its remaining 1600 customers (all in Manhattan) by the end of the year.