Security, human rights, terrorism, poverty, soverignty vs free trade---are some of the many problems. Those problems are part of the challenges of ir today.
Dear Michael, greetings! Your question is very general and wide! If we consider global challenges, then we could say: climate change, huge inequalities between north and south, humanitarian refugees crisis, poverty and hunger.
I think I will agree with many of my colleagues above with respect to trying to narrow your question. It is however interesting to consider global issues.
The challenges and problems of International Realtions todays are enormous and could be discussed in the following ways; Sovereignty of states, Immigration, population explosion in developing countries, terrorism, climate change, racism, poverty, economic wars, arms proliferation, human rights and rule of law among others.