Visitors should obey Ukraine's customs formalities and regulations. When you cross the Ukrainian border you must fill out a customs declaration. It's recommended to declare valuable items and money you bring with you in Ukraine.
You can freely bring money if it doesn't exceed $10,000. If your cash-in-hand is more than $1,000, the sum must be declared in writing. If you need to bring more than $10,000 in cash you will have to obtain a special form from the National Bank of Ukraine. The process can take up to several days. Note that you cannot leave the country with a sum more than stated in the declaration you have filled out upon arrival. The export of local currency is limited to UAH 85. Do not loose your entry declaration, as a custom office has the right to confiscate all your valuable items, including cash.
It's important to remember that one cannot send money through the international mail. Money sent this way can be a subject to confiscation.
You can bring the following items with you in Ukraine duty-free: alcohol (1 liter of spirits and 2 liters of wine); cigarettes (200 cigarettes or 200 grams of tobacco or cigars); foodstuff for private use; personal belongings and toiletries; gifts. Note that only persons over 20 years of age can bring alcohol to Ukraine.
Items of high artistic and historical value cannot be exported without a permission issued by the Ministry of Culture of Ukraine. This applies to art collections or separate works of art, archeological or numismatic items, precious metals and jewels, manuscripts, books published before 1966, furniture made before 1945, hand-made carpets, samovars and some other things. When buying artwork, it's advisable to request a special certificate attesting to its value and artistic significance. The Ministry of Culture office on Prorezna Street can issue such certificates, but the process can be quite complicated.
There is a list of prohibited items you cannot import or export. The list includes weaponry, radioactive and other harmful materials; printed materials, films, records, scripts and other stuff containing propaganda of war, racism, discrimination, etc.; objects prohibited to import or export by Ukrainian laws.
Upon departure from Ukraine your customs declaration will be carefully examined. So it's better not to forget to declare all your valuable items upon arrival and to keep all the receipts for purchases in Ukraine and other countries if you just transit the country.