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We formulate and study a model for inhomogeneous long-range percolation on ${\mathbb{Z}}^d$. Each vertex $x\in {\mathbb{Z}}^d$ is assigned a non-negative weight $W_x$, where ${\left(W_x\right)}_{x\in \mathbb{Z}}^d$ are i.i.d. random variables. Conditionally on the weights, and given two parameters $\alpha ,\lambda gt;0$, the edges are independent and the probability that there is an edge between $x$ and $y$ is given by $p_{xy}=1-exp\{-\lambda W_x{W}_y{/|x-y|}^{\alpha }\}$. The parameter $\lambda$ is the percolation parameter, while $\alpha$ describes the long-range nature of the model. We focus on the degree distribution in the resulting graph, on whether there...