Acoustic metamaterials research has grown exponentially in the past 10 years driven by the advances in manufacturing and an increased understanding of damaging environment noise. 2020 was the first noise reduction target as set by Advisory Council for Aircraft Research and Innovation in Europe with a relative 50% decrease. This was missed by current Jet engine noise control technology; however, metamaterials offer an encouraging alternative. Space Filling Curves (SFC) have the potential to provide a lightweight, thin, high performance acoustic liner. SFC have a history in mathematical geometry dating back to the 1890s but are a comparatively new addition to acoustics. They are designed with a sub-wavelength curled cross-section creating a maze-like pattern which slows acoustic wave propagation through the liner enabling characteristics such as negative refraction and low frequency attenuation. This paper contains a comparison of some of the most promising SFC metamaterial acoustic liner designs, in terms of the fundamental theory of the design category and a discussion of the reflection, absorption and transmission characteristics in terms of a grazing flow conditions. Computer simulation and impedance tube based experimental testing compares the designs. The paper concludes with future application for aeroacoustics with particular focus on the engine inlet.