We report on the experimental evidence of Fano-type guided resonances (GRs) in aperiodically-ordered photonic quasicrystal slabs. With specific reference to the Ammann-Beenker (8-fold symmetric, quasiperiodic) octagonal tiling geometry, we present our experimental results on silicon-on-insulator devices operating at near-infrared wavelengths, and compare them with the full-wave numerical predictions based on periodic approximants. Our results indicate that spatial periodicity is not strictly required for the GR excitation, and may be effectively surrogated by weaker forms of long-range aperiodic order which intrinsically provide extra degrees of freedom (e.g., higher-order rotational symmetries, richer defect states and phase-matching conditions, etc.) to be exploited in the design and performance optimization of nanostructured dielectric slabs operating in the out-of-plane configuration. The essential spectral features may be qualitatively understood in terms of phase-matching conditions derived from approximate homogenized models, and turn out to be effectively captured by full-wave modeling based on suitably-sized periodic approximants. The discovery, in 1984, of "quasicrystals" in solid-state physics 1,2 has triggered a growing interest in the study of aperiodically-ordered structures (based, e.g., on aperiodic tilings 3 ) in many branches of physics and engineering. 4 In particular, photonic quasicrystals (PQCs) have been widely investigated, [5][6][7] with the main focus on in-plane electromagnetic (EM) propagation effects in two-dimensional structures constituted of aperiodically-ordered arrangements of cylindrical inclusions (or holes) in a host medium. In this framework, certain effects observable in periodic photonic crystals (PCs), such as band gap, field localization, negative refraction and super-focusing, directive emission, etc., have been reproduced numerically and experimentally (see, e.g., Refs. 5-7 and references therein). The related studies provided useful insights in the influence of higher-order rotational symmetries, Bragg-type and multiple scattering, and shortrange interactions.8 Moreover, they also envisaged some potential advantages inherently tied to aperiodic order, such as easier achievement of phase-matching conditions, 9 higher isotropy and tradeoff between (lower) dielectric contrast and (higher) rotational symmetry, 10 richer and more wavelengthselective defect states, 11 field-localization capabilities even in the absence of lattice defects, 12 etc. In this framework, novel design strategies especially tailored to exploit the peculiar aspects and further degrees of freedom inherent of aperiodic order have been developed (see, e.g., Refs. 13 and 14).Much less attention has been devoted to out-of-plane propagation effects, with the notable exceptions of arrays of subwavelength holes in metallic films, [15][16][17][18] and arrays of metallic nanoparticles. 19,20 In particular, these latter results indicated the possibility of exciting broad resonances with enhanced spatial locali...