We analyze the entanglement of polymer brushes embedded in long-chain melts and in good and Theta solvents. Individual entanglements are identified using a modified version of primitive path analysis. Due to entropic collapse, the brushes embedded in the melt are more self-entangled than those in the implicit solvents. The self-entanglement of the brushes in the good and Theta solvents as a function of coverage follows a simple scaling argument. We observe a depletion of entanglements near the systems' confining walls and offer several possible explanations. In the melt-embedded systems, the brushes entangle predominantly with the melt at low coverage and with themselves at high coverage. The peak of the brush - melt entanglement density is highest at an intermediate coverage, but the integrated areal brush - melt entanglement density continues to increase with coverage for the studied systems. This areal density correlates well with earlier measurements of the work of adhesion.