Mycelium-based composites are part of an emerging group of biofabricated materials with potential for sustainable construction and interior applications. Their properties depend on fungal species, substrate composition, incubation conditions, and post-processing strategies, yet the relative influence and controllability of these parameters remain fragmented across the literature. This review systematically analyses 46 peer-reviewed studies to evaluate how externally controllable fabrication parameters affect mechanical, thermal, acoustic, and hygroscopic performance. The biofabrication workflow is structured into pre-processing, incubation, and post-processing stages, with particular emphasis on incubation as an underexplored design domain. While species and substrate strongly determine baseline performance, environmental and physical parameters applied during growth, such as moisture, temperature, aeration, and mechanical confinement, suggest potential opportunities for dynamic property tuning. By proposing incubation as an emerging opportunity for material programming, this review outlines pathways toward digitally controlled, functionally graded mycelium composites, contributing a structured framework for integrating biological growth into biodesign workflows.