Citation metrics are increasingly used to appraise published research. One challenge is whether and how to normalize these metrics to account for differences across scientific fields, age (year of publication), type of document, database coverage, and other factors. We discuss the pros and cons for normalizations using different approaches. Additional challenges emerge when citation metrics need to be combined across multiple papers to appraise the corpus of scientists, institutions, journals, or countries, as well as when trying to attribute credit in multiauthored papers. Different citation metrics may offer complementary insights, but one should carefully consider the assumptions that underlie their calculation.