What is the relationship between race and ethnicity? Why are both of these concepts problematic?

What evidence is there to suggest that humans can be divided into discrete races or ethnic groups?
Are there biological foundations to these concepts or are they social constructs (i.e., the product of social discourses and practices)?
How are they important to the cultural social creation of individual and group identity?
What are some of the strengths and limitations of these concepts in understanding human differences?