If your flight was delayed, the airline is responsible (crew shortage, plane scheduling mistakes, maintenance issues), and your plane was late to land by 3 hours or more, you deserve delayed flight compensation.
This applies to flights that originated in the EU* (even if they landed outside it) or inbound flights operated by EU carriers. Flights of up to 1500km are worth €250, from 1500km to 3500km – €400 (the limit for flights taking part completely in the EU), while flights over €3500km go for €600.
Even when the flight is unclaimable, if the wait is longer than 2 hours, the airline should provide care. Seek out the airline personnel at the airport and ask for a free email or free fax, two free phone calls, meals & drinks. For overnight delays, it should give hotel accommodation as well as transport to and from. You should not accept vouchers as they might make ineligible for flight compensation! Also, if you took rerouting offered by the airline (only happens if you miss a connecting flight due to delays) and reached your destination less than 3 hours late, the airline can cut your compensation by 50%.
*EU means the 28 EU Member States and Guadeloupe, French Guiana, Martinique, Reunion, Mayotte, Saint Martin (French Antilles), the Azores, Madeira, the Canary Islands, Iceland, and Norway.
Note that while Ukrainian flight compensation law is roughly similar to Regulation (EC) 261/2004, it does not offer compensation for delayed flights. For example, flight delays that happened on flights leaving Ukraine and operated by Ukrainian-registered airlines will not be compensated.