Recognition of pathogens relies on the diversity of immune receptor proteins. Recent experiments that sequence the entire immune cell repertoires provide a new opportunity for quantitative insight into naturally occurring diversity and how it is generated. The generation process is implemented via a series of stochastic molecular events involving gene choices and random nucleotide insertions between, and deletions from, genes. I will describe how we can attempt to quantify the diversity of the receptors formed in this complex process and point to the origins of diversity in these sequences