A continuing need for improved ecological census methods is emphasized. Three kinds of transect methods are described (line-intercepts, line transects, and strip transects). Variance estimates should be obtained through replicate subsampling. An unbiased estimate for the line-intercept method is proposed, with an example. Two models for the line transect method ("fixed-distance" and "variable-distance") are discussed. The fixed-distance model is essentially the same as that for the line-intercept method. The assumption of random locations of individuals is not needed for estimation. "Group-flushes" pose a problem only if there is a correlation between flushing-distance and group size. A possible bias arising from assumption of a negative exponential distribution model is evaluated by computer simulation. An estimation method derived by D.W. Hayne is shown to be "robust," and a variance estimate suitable for survey design is given. The present line transect methods may not be suitable for inanimate objects, so a non-parametric approach is given. Some of the problems of applying transect theory to marine mammals are described.