In a manufacturing context, the lot-sizing problems (LSP) determine the quantity to produce over a planning horizon. Often, the parameters used in the LSP models are unknown when the decisions are made, and this uncertainty has a critical impact on the quality of the decisions. However, the large amount of data that can nowadays be collected from the shop floor allows inferring information on the LSP parameters and their variability. Therefore, a recent research trend is to properly account for the uncertainty in the LSP optimization models. This work presents a survey on data-driven optimization approaches for the LSPs. We also provide a comparison of some promising optimization methodologies in the context of data-driven modeling of LSPs.