Recent years have seen a surge of econometric development of infill asymptotic theory. Unlike the traditional large-sample theory which assumes that an increasing sample size is due to an increasing time span (denoted as the long-span asymptotic theory in this chapter), infill asymptotic theory assumes that the sample size increases because the sampling frequency shrinks toward zero. The limit of the infill asymptotics of the estimators are those based on a continuous record. Not surprisingly, a development of infill asymptotic theory is closely linked to the increased popularity of continuous time models in applied economics and finance. This chapter reviews the literature on the infill asymptotic theory and applications in financial econometrics, such as unit root testing, bootstrap, and structural break models. In many applications, nonstandard limiting distribution arises. In some cases, the initial condition shows up in the limiting distributions. Monte Carlo studies are carried out to check the performance of the infill asymptotic theory relative to the long-span asymptotic theory.