Kiev is linked with most major European cities and a few in North America. Most international flights go to the puny Boryspil International Airport in Kiev, about 40km (25mi) south-east of the centre. The airport at Lviv, about 8km (5mi) west of its centre, has connections with Warsaw, Prague, Amsterdam, Frankfurt, London and Chicago. Odessa's airport is about 12km (7mi) south-west of downtown, and has flights to and from Vienna and Moscow.
International trains enter Ukraine from seven countries at more than 10 locations. As long as you've got a visa, border crossings are pretty straightforward. Most major Ukrainian cities have daily services from Moscow; it's 15 hours to Kiev and 28 hours to Lviv. You can go between Kiev and Berlin (26 hours) via Warsaw (16 hours) and Brest (10 hours). The station is on the western fringe of downtown Kiev. Lviv has rail connections with most major Eastern European and Russian cities; the station is 3km (2mi) west of the centre. A few buses a day head into Russia from Kharkiv; it takes 20 hours to reach Moscow from Kharkiv by bus.
You can travel by ship between Odessa or Yalta and various cities on the Black Sea and Mediterranean. The main year-round destinations are Haifa (Israel), Limassol (Cyprus), Piraeus (Greece) and Port Said (Egypt). The most frequent and reliable is the Odessa to Istanbul route. It's also possible to sail down the Danube River between Odessa and a number of Eastern European river ports. There's a car ferry running between Kerch, at the eastern tip of Crimea, and the Russian ports of Temryuk, Anapa and Novorossiysk.
All official land border crossings into Ukraine are unrestricted, though they'll always go more smoothly if you have a visa ahead of time rather than relying on getting an emergency visa at the border, especially when entering from Russia.