This document reviews various approaches for designing digital finite impulse response (FIR) filters. It discusses sequential, parallel and symmetric FIR filter architectures implemented using multipliers like Wallace tree and Vedic multipliers. FPGA and ASIC implementations of 8-tap and 16-tap FIR filters are summarized and compared based on parameters like minimum period, maximum operating frequency, area and slice LUTs. Distributed arithmetic and its variants are also evaluated. The review finds that Wallace tree multipliers provide less delay but more area compared to Booth multipliers which offer moderate delay but reduce partial products, enabling high-speed designs.