Summary: A great upsurge in research has taken place during the last decade or so in the area of multiple testing due to its increased relevance in modern scientific investigations. A major portion of this research has been devoted to developing methods that control error rates more meaningful and powerful than traditional ones in the context of these investigations. The error rates measuring false discovery proportions, particulary the false discovery rate (FDR), and procedures controlling them, have received the most attention. This article relates specifically to the FDR and is written with two basic objectives: (i) to put together some important developments in the theory and methodology of the FDR with finite number of hypotheses and report them with newer formulas, proofs and insights, and (ii) to develop an error rate extending the FDR to one that directly incorporates dependence among the test statistics and methods that control it.