Ultrasonic Guided Waves (UGWs) are a useful tool in those structural health monitoring applications that can benefit from built-in transduction, moderately large inspection ranges and high sensitivity to small flaws. This paper describes two methods, based on linear and nonlinear acoustics for structural damage detection based on UGWs. The linear method combine the advantages of UGW inspection with the outcomes of the Discrete Wavelet Transform (DWT) that is used for extracting defect-sensitive features that can be combined to perform a multivariate diagnosis of damage. In particular, the DWT is exploited to generate a set of relevant wavelet coefficients to construct a uni-dimensional or multi-dimensional damage index that, in turn is fed to an outlier algorithm to detect anomalous structural states. The nonlinear acoustics method exploits the circumstance that a cracked medium exhibits high acoustic nonlinearity which is manifested as harmonics in the power spectrum of the received signal. Experimental results also indicate that the harmonic components increase non-linearly in magnitude with increasing amplitude of the input signal. The proposed nonlinear technique identifies the presence of cracks by looking at the harmonics and their nonlinear relationship to the input amplitude. The general framework presented in this paper is applied to the detection of fatigue cracks in an I-shaped steel beam. The probing hardware consists of Lead Zirconate Titanate (PZT) materials used for both ultrasound generation and detection at chosen frequency. The effectiveness of the proposed methods for the structural diagnosis of defects that are small compared to the waveguide cross-sectional area is discussed.