|Abstract||The aim of this paper is to identify and discuss various methods in computational rhythm description of Carnatic and Hindustani music of India, and Makam music of Turkey. We define and describe three relevant rhythm annotation tasks for these cultures - beat tracking, meter estimation, and downbeat detection. We then evaluate several methodologies from the state of the art in Music Information Retrieval (MIR) for these tasks, using manually annotated datasets of Turkish and Indian music. This evaluation provides insights into the nature of rhythm in these cultures and the challenges to automatic rhythm analysis. Our results indicate that the performance of evaluated approaches is not adequate for the presented tasks, and that methods that are suitable to tackle the culture specific challenges in computational analysis of rhythm need to be developed. The results from the different analysis methods enable us to identify promising directions for an appropriate exploration of rhythm analysis in Turkish, Carnatic and Hindustani music.