A polyiamond is an edge-connected set of cells on the triangular lattice. The size of a polyiamond is simply the number of cells it contains. The growth constant of polyiamonds, $\lambda_T$, is the limit of the ratio between the number of polyiamonds of size n+1 and the number of polyiamonds of size n, as n tends to infinity.  In this talk I will show improved lower and upper bounds on $\lambda_T$, proving that it is between 2.8424 and 3.6050.