UPDATE 1220 GMT: The South Korean President's office says Lee Myung-bak has ordered the military to strike North Korea's missile base around its coastline artillery positions if it shows signs of additional provocation.
The spokeswoman added that, in a video conference with Gen. Han Min-koo, Chairman of the Joint Chiefs of Staff, the President ordered "multiple-fold retaliation" against North Korea for its artillery attack today.
UPDATE 1130 GMT: The South Korean military has confirmed its two-day exercise on Yongpyeong Island before the North Korea attack, but it says South Korean forces fired west and not north.
UPDATE 1055 GMT: South Korea has banned its nationals from entering North Korea, including the blocking of a trip to a joint industrial complex in the North Korean border town of Kaesong.
The statement from the President's office: "North Korea's indiscriminate artillery attack on Yeonpyeong Island is a clear military provocation on the Republic of Korea. Furthermore, recklessly shelling against civilians can never be tolerated."
UPDATE 1040 GMT: The English translation of the North Korean military warning: "We will crush you with a fatal blow if South Korea crosses border even by 0.001 millimeter."
UPDATE 1010 GMT: Ah, here's the official North Korean media response: South Korea fired first.
The North Korean military command has also reportedly vowed a "merciless" strike against South Korea.
UPDATE 1000 GMT: As of 0945 GMT, North Korean state media had still not mentioned today's attack; however, an editorial by the Korean Central News Agency has criticised South Korea and the US over their military ties: "It is reported recently that the U.S. is working hard to tighten its alliance for aggression with South Korea in all aspects."
UPDATE 0949 GMT: The South Korean Defense Ministry has said North Korea's barrage is an "intentional and planned attack" and a clear violation of the 1953 armistice.
UPDATE 0945 GMT: The White House has "strongly condemned" the North Korean attack and says it is "firmly committed" to the defence of its ally South Korea.
UPDATE 0931 GMT: South Korea has indefinitely postponed Red Cross talks with North Korea. The next discussions were to be on Thursday.
UPDATE 0929 GMT: A second South Korean soldier has died of wounds suffered during the North Korean barrage.
UPDATE 0925 GMT: Video, from the South Korean mainland, of Yeonpyeong Island during the North Korean artillery attack:
UPDATE 0920 GMT: A South Korean official has warned of "stern retaliation" against North Korea if there is "additional provocation".
UPDATE 0915 GMT: A local official says Yeonpyeong Island was hit by at least 50 artillery shells. Mountains and homes are still on fire.
A spokesman for Incheon Metropolitan City, to which Yeonpyeong Island belongs, said at least four civilians were wounded.
UPDATE 0800 GMT: A Chinese official, speaking on Al Jazeera English, has called on both North and South Korea to "calm down" and "disengage".
An assistant to US Secretary of State Hillary Clinton has said that she has spoken to China and Japan. The American official says Beijing wants an immediate restart of six-party talks over regional issues and North Korea's nuclear programme.
UPDATE 0740 GMT: One South Korean soldier has died from his injuries.
UPDATE 0725 GMT: Meeting in emergency session, South Korean President Lee Myung-bak has instructed his senior officials to pursue a restrained response to the North Korean artillery fire: "(We) should carefully manage the situation to prevent the escalation of the clash."
UPDATE 0720 GMT: Witnesses now say the shelling appears to have stopped.
There are reports this morning of "at least 200" North Korean artillery shells being fired at the South Korean island Yeonpyeong, bringing return fire of about 80 shells. Witnesses say houses are on fire and have collapsed, and residents are leaving the island in fishing boats. Four South Korean soldiers have been seriously wounded and ten lightly wounded. Two civilians have also been injured.
South Korea is now on its highest level of "non-war alert". Fighter jets have been deployed off the west coast.
Yeonpyeong is off the northwest coast of South Korea, near the North Korean border. It has about 600 homes and 1000 residents.
South Korean military forces had been conducting a two-day exercise on and around the island, possibly including artillery fire, and had been warned by North Korea to desist. The North Korean attack started soon after the end of the exercise.