Cuneiform tablets from the Late-Babylonian period (400-50 BCE) contain the earliest known form of mathematical astronomy in the ancient world. The tablets can be divided into approximately 360 tables with computed data for the Moon and the planets, and approximately 110 procedure texts with corresponding computational instructions (for the latter cf. Ossendrijver 2012, ‘Babylonian Mathematical Astronomy: Procedure Texts’). A distinctive feature of Babylonian astronomical tables is that their columns contain not only final results, i.e. empirically meaningful quantities that do not serve as input for further computations, but also numerical data pertaining to intermediate steps of the underlying algorithms. The reconstruction of the algorithms underlying Babylonian astronomical tables therefore proceeds by analysing the individual columns and the possible connections between them. I begin this paper by discussing some of the existing methods for analysing Babylonian astronomical tables that were developed by Otto Neugebauer and other pioneers of the field, and the ways in which these methods have affected our view of Babylonian mathematical astronomy and its conceptual framework. As I will argue,certain distortions resulting from the strong emphasis by the pioneers on using modern mathematics for table crunching have begun to be corrected only in recent years. I will then discuss some of the more recent methods for tabular analysis that have become possible only with the advent of modern computers.