If you are adopting a child from another country, I strongly urge you to check the US Office of Children's Issues website about country specific information. This information is easy to find, and is something all families wanting to adopt internationally should be looking for. On that website you will find all the information about the dossier requirements, along with all the other specifications for the particular country you're interested in.
As an example, you can go look at the page about Serbia, since a few people have contacted me about that country in particular. Also, the information to contact the ministry directly is posted. The Ministry of Serbia wants all information regarding Serbian adoptions to be 100% transparent. I would further urge you to check out the information about "Who Can Be Adopted". If your agency is telling you something different about the children available, you need to ask some questions.
Since I have been asked about Serbia specifically, and I have adopted a child from there, I'll address that here. Serbia is a wonderful country to adopt from, and the government has made it extremely low cost, with the only fee charged being the issuance of a passport. (approximately $25 US depending upon the exchange rate.) The only fees you're expected to pay within country are not to any particular agency, but are for documents such as the new birth certificate, (just like here in the US if you need to get a copy of a birth certificate, it is not free.) passport, medical exam, visa photos and the visa itself. (the medical exam is required to get a US Visa and is about $100 USD, and the Visa is $400 which is a US fee, not a Serbia fee.) You will need to travel to the city where the child was born to complete the adoption with the local ministry officials there. You can expect to pay your own transportation costs. There are NO other fees to pay within Serbia.
*edited to add: As pointed out by Kaci in the comments, I neglected to include translation fees for an authorized court translator of YOUR choosing. The Ministry will give you a list of approved translators if you request it.
Your visits with the child will be observed by the child's social workers (There were three who observed my visits with Axel) for several days before you will be asked if you are sure this child will fit your family, etc. A report is then written and submitted to the head ministry department in Belgrade for final approval. Once the ministry has given final approval, then the adoption can proceed. There is no "court". In other words, you don't appear before a judge, but you DO appear before the entire social services agency, and there are many legal documents to sign and declare, all of which will be presented to the US Embassy to look over before the child's visa can be issued.
Please check out the website listed above for the information related to the country you're interested in adopting from. Make sure the agency you're working with is following the laws of that country. Don't assume that because they've said they've met with ministry officials that they actually have. If the website lists direct government contact information for the country you're researching, by all means, make the contact and ask questions.