So consider two random variables $X$ and $Y$ with PDF's $f_X$ and $f_Y$. When both are independent the PDF of $X+Y$ simply becomes the convolution product $f_X*f_Y$.
However what if these are not independent? Is there some alternate formula one can turn to, possibly using the conditional PDF of $Y$ wrt $X$? If no such clear cut answer exist, are there general approaches one can use to find the PDF $f_{X+Y}$?