There are many challenges to cross-cultural communications. Let me list a number of them for you.
First, the most obvious challenge is the language barrier. This is a real difficulty, because not many people are multi-lingual. And even if a person speak two or three languages fluently, the world is a smaller place, that is, business is conducted in many different languages.
Second, there are cultural difficulties as well. Sometimes this is a greater challenge, because people can overlook the language barriers. But when cultural barriers are broken, people can get offended. For example, in Asian culture it is important to respect your elders; in Western cultures, this is not as important.
Third, expectations and the way of doing things are also different when it comes to cultures. For instance, in non-Western cultures, relationships are the most important, rather than infrastructure or even profits. This is a paradigm shifting point.