In many cases, the level, positioning and timing of signaling through the bone morphogenetic protein (BMP) pathway are regulated by molecules that bind BMP ligands in the extracellular space. Whereas many BMP-binding proteins inhibit signaling by sequestering BMPs from their receptors, other BMP-binding proteins cause remarkably context-specific gains or losses in signaling. Here, we review recent findings and hypotheses on the complex mechanisms that lead to these effects, with data from developing systems, biochemical analyses and mathematical modeling.