Vibration-based structural damage detection constantly involves uncertainties, including measurement noise, methodology, and modeling errors. Bayesian inference provides a rigorous framework to consider uncertainties and obtain probabilistic solutions. In recent decades, sparse Bayesian learning (SBL) and the closely related automatic relevance determination model have been extensively used, resulting in sparse solution. Given that damage typically occurs in limited sections or members, particularly at the early stage of structural failure, the SBL method is developed for structural damage detection using vibration data. However, analytical posterior probability density function is unavailable owing to the high-dimensional integral in the evidence and nonlinear relationship between the measured modal and structural parameters. Therefore, a range of techniques are utilized to obtain solutions based on analytical approximations or numerical sampling, including the expectation–maximization, Laplace approximation, variational Bayesian inference, and delayed rejection adaptive metropolis techniques. Numerical and experimental examples demonstrate that the proposed SBL method can accurately locate and quantify sparse damage. In addition, the mechanisms, advantages, and limitations of different analytical and numerical techniques are described and compared, and the corresponding suggestions for their applications are proposed.