In the last three decades it has become quite common to evaluate local muscle fatigue by means of surface electromyographic (sEMG) signal processing. A large number of studies have been performed yielding signal-based quantitative criteria of fatigue in primarily static but also in dynamic tasks. The non-invasive nature of this approach has been particularly appealing in areas like ergonomics and occupational biomechanics, to name just the most prominent ones. However, a correct appreciation of the findings concerned can only be obtained by judging both the scientific value and practical utility of methods while appreciating the corresponding advantages and limitations. The aim of this paper is to serve as a state of the art summary of this issue. The paper gives an overview of classical and modern signal processing methods and techniques from the standpoint of applicability to sEMG signals in fatigue-inducing situations relevant to the broad field of biomechanics. Time domain, frequency domain, time-frequency and time-scale representations, and other methods such as fractal analysis and recurrence quantification analysis are described succinctly and are illustrated with their biomechanical applications, research or clinical alike. Examples from the authors' own work are incorporated where appropriate. The future of this methodology is projected by estimating those methods that have the greatest chance to be routinely used as reliable muscle fatigue measures.