Michael Fay gave a short course on interval censored data at the 2010 useR! meeting. The slides from this short course provide a nice overview of the complexities of this type of data.
Michael P. Fay. Interval Censored Data Analysis. useR! 2010 meeting. Available at https://www.r-project.org/conferences/useR-2010/tutorials/Fay.html.
You can find an earlier version of this page on my blog.