Under the notion of list decoding, the decoder is allowed to output a small list of codeword such that the transmitted codeword is present in the list. Even though combinatorial limitations on list decoding had been known since the 1970's, there was essentially no algorithmic progress till the breakthrough works of Sudan and Guruswami-Sudan in the mid to late 1990's. There was again a lull in algorithmic progress till a couple of recent papers closed the gap in our knowledge about combinatorial and algorithmic limitations of list decoding (for codes over large alphabets). This article surveys these latter algorithmic progress.