The simulation-based inference is a powerful approach that can deal with various challenges ranging from discovering hidden properties to simulation algorithms tuning and optimising device configurations. Such methods as evolutionary algorithms or Bayesian optimisation usually help to address those challenges. However, those approaches rely on assumptions that might not hold. Recently, a series of methods have been introduced to estimate black-box gradients that significantly speed up the optimisation process. This talk outlines such methods: REINFORCE-based, variational optimisation and surrogate generative model-based approaches. We provide theoretical intuition for those methods as well as practical illustrations of their strengths and weaknesses. Such comparison will help practitioners to understand those methods and apply them to the inference tasks of their domains of interest.