Multiple systems estimation refers to a class of inference procedures that are commonly used to estimate the size of hidden populations based on administrative lists. In this paper we discuss some of the common challenges encountered in such studies. In particular, we summarize theoretical issues relating to the existence of maximum likelihood estimators, model identifiability, and parameter redundancy when there is sparse overlap among the lists. We also discuss techniques for matching records when there are no unique identifiers, exploiting covariate information to improve estimation, and addressing missing data. We offer suggestions for remedial actions when these issues/challenges manifest. The corresponding R coding packages that can assist with the analyses of multiple systems estimation data sets are also discussed.