Thin-film (TF) based dispersion compensators are of necessity some form of allpass filter. Whether these allpass filters are cast in the form of a coupled or a cascaded cavity structure, they can provide compact, low-loss, and highly stable dispersion compensation thereby having the potential of becoming important future components in both optical time-division multiplexing (OTDM) and wavelength division multiplexing (WDM) systems. In this paper, the salient points in the development of these devices are discussed up to the present state of the technology. Particular emphasis is placed on TF coupled cavity allpass (CCAP) filters as devices that provide only third-order dispersion compensation (TODC), having a group delay response that is purely quadratic. These CCAP filters are shown to have evolved over a number of important steps, from a hybrid two-cavity device, to a completely TF two-cavity single-surface filter, and finally to a dual-surface multi-reflection four-cavity device. The adjustable hybrid coupled cavity allpass filter provides TODC between 2.0 and 15.5 ps3 over a bandwidth between 3.6 and 1.2 nm respectively with a center wavelength tunable over an 8 nm range and the four-cavity multi-reflection completely TF device offers TODC between 0.37 ps3 and 3.2 ps3 over a 10 nm bandwidth with a center wavelength tunable over a 10 nm range. Important issues, such as the need to increase the TODC figure of merit, which is directly proportional to the number of cavities and the number of surface reflections, of these devices without incurring large loss penalties are discussed in the context of some of the important technological challenges that need to be addressed and solved before TF dispersion compensators can be effectively employed in optical systems as well as successfully compete with other existing dispersion-compensation technologies.