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We review theoretical studies of the attosecond streaking time delay concept in photoionization via the investigation of the electron dynamics in the streaking field after the transition of the photoelectron into the continuum upon absorption of an extreme ultraviolet photon. Based on the results, a so-called finite range interpretation was introduced, which highlighted that the delay is accumulated until the streaking pulse ends and, hence, over a finite range of the potential of the parent ion. Following a discussion of the analysis leading to this interpretation, we summarize a few applications which provide insights into different aspects of the streaking time delay concept in photoionization. Besides a review of previously presented results, we give an analysis of the relevance of the first half-cycle of the streaking field and an outlook regarding the perspective of using the streaking method to resolve dynamical changes in the potential that the photoelectron explores during its propagation in the continuum.