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Adaptive Digital Filters (ADFs) are computationally demanding Digital Signal Processing (DSP) systems with applications in diverse areas signal processing, such as active noise control, channel equalization, system identification. The most popular implementation structure for ADFs is FIR transversal filter which can be efficiently implemented without multipliers by Distributed Arithmetic (DA) method. DA is used to efficiently implement digital FIR filter with a precomputed weight DA combinations in a memory element. However, due to the operation of ADFs the memory content has to be recomputed at each iteration; the advantage of DA method disappears. The objective of this review is to cover the research gap on DA-ADF implementations. This article reviews the main features and contributions of DA-ADF designs present in literature. The DA-ADF designs have been grouped into three categories: non-pipelined, pipelined and block processing. Pipelining and block processing increase the throughput of the ADF. The reviewed designs implement only Least Mean Square (LMS) type adaptive algorithms due to the simplicity of implementation. Latest and most efficient designs tend to employ conjugate Offset Binary Coding (OBC) DA structure.