This text targets a review of the computational analysis literature for Turkish makam music, discussing in detail the challenges involved and presenting a perspective for further studies. For that purpose, the basic concepts of Turkish makam music and the description of melodic, rhythmic and timbral aspects are considered in detail. Studies on tuning analysis, automatic transcription, automatic melodic analysis, automatic makam and usul detection are reviewed. Technological and data resource needs for further advancement are discussed and available sources are presented. Osmanlı/Türk (sanat) musikisi') and exclude folk and popular genres, while most of our discussions would still find some relevance for these excluded genres. When we provide analysis results to demonstrate an approach, the data sets used include pieces from a time span of 3-4 centuries from composers like Itri, İsmail Dede Efendi, Hacı Arif Bey, Tanburi Cemil Bey and Sadettin Kaynak. 2 We use the spelling "makam" here, which is used in Turkey, because we mainly refer to the concepts of music traditions practiced nowadays in Turkey. 3 Yekta cites the following reference for this definition: Dechevrens, A. (1898). Etudes de science musicale. 1-11, Paris. 4 The terms like çeşni, güçlü, karar and seyir are explained in various sections of the text. In addition short descriptions are provided in the glossary section at the end. 11 Signell's book (Signell, 2008) presents most of the crucial parts of this theory in a compact form. 12 We use this term because we want to avoid the misleading dichotomy of Western and non-Western music. 13 Should be Uşşak flavor. Unfortunately the eager effort of the renowned master Murat Aydemir is overshadowed by occasional errors in the representation. 14 Should be Rast flavor with acem pitch. This error is possibly due to a translation error.