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Black-box topology optimization (BBTO) uses evolutionary algorithms and other soft computing techniques to generate near-optimal topologies of mechanical structures. Although evolutionary algorithms are widely used to compensate the limited applicability of conventional gradient optimization techniques, methods based on BBTO have been criticized due to numerous drawbacks. In this paper, we discuss topology optimization as a black-box optimization problem. We review the main BBTO methods, discuss their challenges and present approaches to relax them. Dealing with those challenges effectively can lead to wider applicability of topology optimization, as well as the ability to tackle industrial, highly-constrained, nonlinear, many-objective and multimodal problems. Consequently, future research in this area may open the door for innovating new applications in science and engineering that may go beyond solving classical optimization problems of structural engineering. Furthermore, algorithms designed for BBTO can be added to existing software toolboxes and packages of topology optimization.