This paper presents a survey of two basic puzzles in international finance. The first puzzle is the `predictable excess return puzzle.' The returns on foreign currency deposits relative to domestic currency deposits should be equalized based upon uncovered interest parity. However, not only do researchers find that deviations from uncovered interest parity are predictable ex ante, but their variance exceeds the variance in expected exchange rate changes. In the paper, I describe different explanations of this phenomenon including the view that excess returns are driven by a foreign exchange risk premium, peso problems or learning, and market inefficiencies. While the research to date has been able to better define the `predictable excess return puzzle' and to suggest the most likely directions for future progress, no one explanation has provided a full answer to the puzzle. The second puzzle is the `home bias puzzle.' Empirical evidence shows that domestic residents do not diversify sufficiently into foreign stocks. This evidence is clear whether looking at models based on portfolio holdings or outcomes of consumption realizations across countries. In this paper, I examine several possible explanations including non-traded goods and market inefficiencies, although even after considering these possibilities, the puzzle remains.