Ever since the end of the Second World War there have been large numbers of children adopted each year from overseas by families in the USA. Often these numbers have spiked following a disaster or war: thousands of German children in the 1940s and 1950s; South Korean children in the 1950s and 1960s; Vietnamese children by their thousands in the mid-1970s and “Operation Babylift” in 1975; children from El Salvador and Guatemala in the 1980s; and Romanian and Russian children following the fall of the Iron Curtain in the 1990s. As Pricenomics notes:

“These figures are a strange lens through which to view the American public’s changing understanding of the world. But the fact that American adoption trends tend to track with conflict, disaster, and destitution also reflects a fairly obvious point: Americans adopt orphans from countries that are full of adoptable orphans.” 

From 1950-ish until 2004 the number of international adoptions by Americans rose steadily. In 2004, nearly 23,000 children were adopted from abroad. Since then, there has been a steep decline in these numbers. Last year, the number was 5,647, a 75% decline in ten years. And this applies not just to the USA; the number of international adoptions by the largest 15 “receiving” countries has dropped in the years 2004-2014 by between 35% (Italy) and 91% (Ireland). Most of these nations have seen their international adoption numbers decline by over 60%. 
So why have these numbers dropped so dramatically? Partly because many of the “sending” countries, like China, have adopted the Hague Convention on the Protection of Children and Co-operation in Respect of Intercountry Adoption. These countries, and NGOs like UNICEF, have promoted an interpretation of the treaty which considers that international adoption should be considered only when all other alternatives have been tried. There has been an increase in restrictions such as mandatory waiting periods, residency requirements for adoptive parents and “instructions that social service authorities seek domestic adoption, domestic fostering, and even informal arrangements with extended family members before considering foreign parents”.
It should be noted that such guidelines and the prioritisation of domestic custody is the way that many receiving countries (including Canada, Italy, Sweden, Greece) treat their own abandoned and orphaned children. Further, in many countries (such as Romania) horror stories of abuse and exploitation emerged over the years – the Hague Convention was to help governments deal with such issues. However, for some countries the new policy is a way of announcing to the world that “we are no longer a third world country: we can take care of our own kids and don't need you any more." Geopolitics also plays a role in the drop off of international adoptions: in 2012 the Russian government imposed an absolute adoption ban on all US citizens. While this was in response to a the death of a Russian-born toddler in the custody of his adoptive father, many saw it as an act of retaliation against American financial sanctions from earlier that year. 
Behind all of this is ambivalence: is it really in the best interests of children to be adopted by families from another country and to grow up outside of their native culture and wider support networks (if any)?
Elizabeth Bartholet, faculty director of the Child Advocacy Program at Havard Law School argues that the answer is an emphatic “yes”: 

“That drop-off represents the tens of thousands of kids every year who used to get loving, nurturing homes and now aren’t getting them...I think it’s rank hypocrisy to talk as if these [restrictions on adoptions] are justified in terms of the child’s best interest.” 

On the other hand, thousands of Korean adoptees have joined together to push for greater restrictions on adoptions and more financial support and social acceptance for unwed mothers. Kim Stoker, an anti-adoption advocate argues: 

“I don’t think it’s normal adopting a child from another country, of another race and paying a lot of money... I don’t think it’s normal to put a child on a plane away from all its kin…it’s a very modern phenomenon.” 

All things being equal, it is probably better that a child stays in its own culture and near its own family, but that assumes that they have a family willing to adopt them in in their home country and aren't to be left in an orphanage or institution. 
Finally, it should be noted that, while domestic adoptions have declined since the 1970s due to birth control, abortion, falling fertility rates and the rise of single-parent households, there are still over 100,000 children waiting to be adopted in the USA. Some 87 percent of these 100,000 were at least two years old and over half of those children were not white. Hopefully, some of those Americans who cannot adopt form overseas will look closer to home to give these children a chance at a family life.