This paper gives a survey and comparison of algorithms for the detection of binary data in the presence of two-dimensional (2-D) intersymbol interference. This is a general problem of communication theory, because it can be applied to various practical problems in data storage and transmission. Major results on trellis-based detection algorithms, previously disparate are drawn together, and placed into a common framework. All algorithms have better complexity than optimal detection, and complexity is compared. On the one hand, many algorithms perform within 1.0dB or better of optimal performance. On the other hand, none of these proposed algorithms can find the optimal solution at high SNR, which is surprising. Extensive discussion outlines further open problems.