A number of works titled Sankaravijaya, or Sankara digvijaya, are extant in India. These are typically known after the names of their authors, but are mostly hagiographic accounts of Sankara's life, with myth and legend interspersed with historical fact. The primary reason for this situation is that most of these texts were written many centuries after Sankara lived, so that these authors already regarded Sankara as a legendary figure. The following is a brief survey of these texts.
mAdhavIya Sankaravijaya - The mAdhavIya is probably the oldest available, and also the most authentic and widely known among the different Sankaravijayas today. It is certainly the most popular such text in the advaita tradition, and is also known as the sam.kshepa Sankarajaya. The popularity of this work derives from the fame of its author, mAdhava, who is usually identified with vidyAraNya, the 14th century maThAdhipati at Sringeri. Old manuscripts of this work are available from diverse places in India, and printed editions based on a comparison of various manuscripts are available from as early as 1863 CE.  Two commentaries have been written to the mAdhavIya, one titled DiNDimA, by dhanapati sUrI (composed in 1798 CE), and another titled advaitarAjyalakshmI by acyutarAya (composed in 1824 CE). There are a couple of good English translations of the mAdhavIya, one by swAmI tapasyAnanda of the Ramakrishna Math,  and another by K. Padmanabhan.  Contemporary accounts of Sankara's life follow this text in most details, e.g. birth in Kaladi, meeting with his guru on the banks of the river Narmada, writing of commentaries, debate with maNDana miSra, establishment of the SAradA temple at Sringeri, ascension of thesarvajnapITha in Kashmir and his last days in the Himalayas.
There has been some doubt in recent times about the date and authorship of the mAdhavIya Sankaravijaya,  including charges that it was reworked extensively in the 19th century CE. Almost all of this criticism is baseless. If the author of this work is not identical with vidyAraNya, the latest date that can be put to it is 1798 CE, the year in which the DiNDimAcommentary was completed. Moreover, another author, sadAnanda, who wrote a Sankaravijaya sAra in 1783, informs us that his source is mAdhava's work. As such, the criticism that the mAdhavIya was written as late as the 19th century CE, or that portions of it were re-written recently, cannot be upheld. swAmI tapasyAnanda is correct in dismissing such criticism as nothing more than "bazaar gossip."  However, the earliest possible date of this work (14th century CE) is still several centuries later than Sankara's own date. Some modern historians who doubt that Sankara established any maThas at all, attribute the origin of the tradition of four AmnAya maThas to mAdhava.  However, it must be noted that the mAdhavIya Sankaravijaya gives only a general description of the establishment of maThas, at Sringeri and other places, but does not specifically mention the number four.
AnandagirIya Sankaravijaya - This work is not available today, although according to many secondary sources, it must have existed at one time. It is attributed to Anandagiri, the 13th century author of well-known TIkAs to SankarAcArya's bhAshyas. One 19th century author, who wrote a commentary to the mAdhavIya refers to Anandagiri's Sankaravijaya as bRhat Sankaravijaya in one place and as prAcIna Sankaravijaya in another place. It seems clear that this text was considered to be old (prAcIna) and huge (bRhat). However, as it is no longer extant, the quotations attributed to this text are not very trustworthy.
In recent times, there have been various claims about a bRhat Sankaravijaya of an author named citsukha, although no manuscripts of this work have ever been available. No secondary sources refer to this text either, unlike the case with Anandagiri's text. citsukha is claimed to have been a childhood friend of Sankara's, and his work is therefore claimed to be an authoritative eye-witness account. However, even the source for this story about citsukha remains unknown, as none of the other Sankaravijayas mention such a childhood friend who witnessed all of Sankara's life. All claims about the bRhat Sankaravijaya of citsukha seem extremely far-fetched, and within the living advaita tradition, there is great controversy over the very existence of this text. There is a more recent text, called bRhat Sankaravijaya, by one brahmAnanda sarasvatI, which seems to date from the 17th or 18th century.
Another prAcIna Sankaravijaya is also sometimes attributed to one mUkakavi. As with the bRhat Sankaravijaya of citsukha, nothing specific is known about this prAcIna Sankaravijaya either, as all attempts to trace source manuscripts have failed. Some quotations from a prAcIna Sankaravijaya are found in some very recent works, but the real source of these quotations remains unknown.