RS codes are in ubiquitous use because of their good correction capabilities against errors 
caused by stationary and burst noise and the availability of efficient algebraic hard-
decision decoding (HDD) technology. Achieving additional performance gains by employing 
soft decision RS decoding instead of HDD is an obvious objective. Following a discussion 
of theoretically achievable gains, an overview of soft/list RS decoding methods is given. 
A first part is devoted to early reliability based soft/list decoding algorithms and 
refinements thereof. This includes GMD- and Chase-type algorithms, which perform hard 
decision decoding with variations of the least reliable received symbols, and OSD 
algorithms, which are focusing on re-encoding information sets formed from the most 
reliable received symbols with several variations. A second part addresses soft/list 
decoding based on extending the standard Berlekamp-Massey algorithm beyond known syndromes. 
A third part deals with interpolation-based algorithms such as Koetter-Vardy. A simplified 
version with Chase-type variations of the least reliable symbols is also discussed. In a 
fourth part iterative soft decoding based on belief propagation is addressed. 

The general conclusion is as follows: The binary images of high-rate RS codes are random-
like binary codes which in principle permit approaching capacity if affordable MLD 
algorithms would exist. With the variety of soft RS decoding methods developed over the 
years significant improvements over HDD are achieved for short codes. However, gains 
diminish rapidly for longer codes while complexity soars. The search for more efficient 
soft RS decoding methods continues.