Consider a large $n \times n$ random matrix $Y_n$ with entries given by $Y_{ij} = \frac{\sigma_{ij}}{\sqrt{n}} X_{ij}$ where the $X_{ij}$'s are independent and identically distributed random variables with four moments, and the $\sigma_{ij}$'s are deterministic, non-negative quantities and account for a variance profile. Notice that some of the $\sigma_{ij}$'s may be equal to zero. In this talk, we will describe the limiting spectral distribution of matrix $X_n$ as $n \rightarrow \infty$, that is the limit of the empirical distribution of $X_n$'s eigenvalues. We will carefully specify the assumptions on the variance profile $(\sigma_{ij} )$ under which we can describe the limiting spectral distribution. This is a joint work with Nicholas Cook, Walid Hachem and David Renfrew.