Approximate string matching is fundamental to bioinformatics, and has been the subject of numerous FPGA acceleration studies. We address issues with respect to FPGA implementations of both BLAST-and dynamic-programming-(DP) based methods. Our primary contributions are two new algorithms for emulating the seeding and extension phases of BLAST. These operate in a single pass through a database at streaming rate (110 Maa/sec on a VP70 for query sizes up to 600 and 170 Maa/sec on a Virtex4 for query sizes up to 1024), and with no preprocessing other than loading the query string. Further, they use very high sensitivity with no slowdown. While current DP-based methods also operate at streaming rate, generating results can be cumbersome. We address this with a new structure for data extraction. We present results from several implementations.