Ukraine is not a member of NATO, but it is a NATO 'partner'. In fact, it has had co-operation agreements with NATO since it became an independent state in 1991.
It applied to become a full member under the presidency of Viktor Yushchenko, who came to power in 2005 after the so-called Orange Revolution. And in April 2008, at a summit in Bucharest, NATO decided in principle that Ukraine (and Georgia) should become full members. The declaration agreed at the summit stated:
"NATO welcomes Ukraine's and Georgia's Euro-Atlantic aspirations for membership in NATO. We agreed today that these countries will become members of NATO."
But neither state has actually joined. Thanks to opposition from Germany, France and others at that summit, neither state was allowed to embark on the next step towards membership, which is the drawing up of a Membership Action Plan (MAP).
In June 2010, after Viktor Yanukovych was elected president, Ukraine withdrew its application for NATO membership. The Ukrainian Parliament approved a bill which excluded the goal of "integration into Euro-Atlantic security and Nato membership" from Ukraine's national security strategy and committed it to "a non-bloc policy which means non-participation in military-political alliances".
This seems to be in line with popular opinion in Ukraine today - a Gallup poll in June/July 2013 found that respondents were much more likely to regard NATO as a "threat" (29%) than as "protection" (17%).
Although Ukraine made a decision in 2010 not to become a NATO member, it remains a NATO 'partner', as are all former Soviet republics, including Russia itself. 'Partners' engage in various forms of cooperation with NATO, for instance, joint military exercises, supplying troops to NATO operations.
Today, NATO has 28 member states. At the end of the Cold War, it had 16: since then, another 12 have been added, all in eastern Europe, despite promises made to the Soviet Union that NATO would not expand eastwards. As the last leader of the of the Soviet Union, Mikhail Gorbachev, said in an interview with The Daily Telegraph on 7 May 2008:
"The Americans promised that Nato wouldn't move beyond the boundaries of Germany after the Cold War but now half of central and eastern Europe are members, so what happened to their promises? It shows they cannot be trusted."
Under Article 5 of NATO's founding treaty, if any one of these 28 members is subject to an armed attack, NATO is supposed to rush to its defence.
In addition, since the end of the Cold war, NATO has acquired 22 'partner' states, stretching from Ireland in the west to Kyrgyzstan in the east. Unlike full members, they are not promised assistance under Article 5 if they are attacked.