Surface waves bounded by subwavelength-structured surfaces have many exotic electromagnetic properties different from those supported by smooth surfaces. However, there is a long-standing misconception, claiming that these waves must propagate along the macroscopic interface. In this paper, we describe in detail the microscopic meta-surface wave (M-wave) in artificial subwavelength structures. It is shown that the waves penetrating macroscopic surfaces share the essence of most surface waves (i.e., they spread along the microscopic interfaces, formed by adjacent constitutive materials). Equivalent circuit theory and transfer matrix method have been adopted to quantitatively describe these M-waves with high accuracy in the form of catenary optical fields and dispersion. Based on these analyses, novel omnidirectional band-stop filters and wide-angle beam deflectors are designed with operational angles up to 88°. We believe these results may provide many new perspectives for both the understanding and design of functional subwavelength structures.