Lithium-ion batteries (LIBs) are used extensively worldwide in a varied range of applications. However, LIBs present a considerable fire risk due to their flammable and frequently unstable components. This paper reviews experimental and numerical studies to understand parametric factors that have the greatest influence on the fire risks associated with LIBs. The LIB chemistry and the state of charge (SOC) are shown to have the greatest influence on the likelihood of a LIB transitioning into thermal runaway (TR) and releasing heats which can be cascaded to cause TR in adjacent cells. The magnitude of the heat release rate (HRR) is quantified to be used as a numerical model input parameter (source term). LIB chemistry, the SOC, and incident heat flux are proven to influence the magnitude of the HRR in all studies reviewed. Therefore, it may be conjectured that the most critical variables in addressing the overall fire safety and mitigating the probability of TR of LIBs are the chemistry and the SOC. The review of numerical modeling shows that it is quite challenging to reproduce experimental results with numerical simulations. Appropriate boundary conditions and fire properties as input parameters are required to model the onset of TR and heat transfer from thereon.