The ongoing revolution in life sciences research is producing vast amounts of genetic and proteomic sequence data. Scientists want to pose increasingly complex queries on this data, but current methods for querying biological sequences are primitive and largely procedural. This limits the ease with which complex queries can be posed, and often results in very inefficient query plans. There is a growing and urgent need for declarative and efficient methods for querying biological sequence data. In this paper, we introduce a system called Periscope/SQ which addresses this need. Queries in our system are based on a well-defined extension of relational algebra. We introduce new physical operators and support for novel indexes in the database. As part of the optimization framework, we describe a new technique for selectivity estimation of string pattern matching predicates that is more accurate than previous methods. We also describe a simple, yet highly effective algorithm to optimize sequence queries. Finally, using a real-world application in eye genetics, we show how Periscope/SQ can be used to achieve a speedup of two orders of magnitude over existing procedural methods!