Primarily through synthetic and field data examples, this paper reviews the benefits of recent developments in time migration of seismic data and reveals limitations, some of them fundamental, that keep elusive the goal of imaging steep events with full accuracy. Even where velocity varies only with depth and, hence, time migration should suffice, accurate imaging of very steep events requires that the velocity structure be known with considerable precision and be finely sampled in depth. This sensitivity of migration accuracy to detail in velocity structure is attributable to the sensitivity of ray bending for wide-angle rays to detail in the velocity structure. Also, interestingly, the presence of ray bending at interfaces is seen to enhance the steep-event accuracy of some algorithms (e.g., phase shift and cascaded finite-difference) while it degrades the accuracy of others (for example, conventional Kirchhoff summation and the frequency-wavenumber domain method of Stolt). Of the various time-migration schemes, a cascading of the Stolt method is the most efficient while having steep-event accuracy in the presence of significant vertical velocity variation. Its behavior in the presence of even mild lateral velocity variation, however, differs greatly from that of the other methods and must be taken into account.A case involving 3-D migration of 3-D survey data shows how different issues in imaging of the subsurface (two-pass versus single-pass 3-D migration and algorithm choice in the presence of mild lateral velocity variation) can become intertwined in practice and lead to confusion as to which of the issues is essential for accurate imaging of the subsurface.