Kansai International Airport (KIX) is the main international gateway, connected to Osaka by the Haruka limited express train (70 minutes to Shin-Osaka or 50 minutes to Tennoji) or the faster Nankai Rapi:t express to Namba (37 minutes). Itami Airport (ITM), closer to the city, handles mostly domestic flights.
By shinkansen, Osaka is served by Shin-Osaka Station (the northern terminus of the Tokaido Shinkansen), one stop from central Osaka. Tokyo is 2.5 hours; Hiroshima is 1 hour; Hakata (Fukuoka) is 2.5 hours. From Kyoto, ordinary express trains run every few minutes and take 15 minutes to Osaka Station.
Long-distance bus services from Tokyo and other Japanese cities arrive at the Osaka City Air Terminal (OCAT) near Namba Station; overnight services are cheaper than the shinkansen if time is flexible.