This talk begins with introducing the structural credit risk model of Merton (1974), and with which one can define the distance-to-default (DTD) measure. I will discuss the conceptual advantage of using DTD as opposed to leverage. The Merton model relies on the use of the the asset value dynamic, but the market value of firm's assets cannot be directly observed. This challenge has generated a literature on ways of implmenting the Merton model. I will introduce several ad hoc methods and discuss their shortcomings and/or limitations. A popular way of estimating DTD in the academic literature and the industry applications is the KMV method. I will describe this method and its limitations, particularly in terms of its application to financial firms. In addition, I will introduce the transformed-data maximum likelihood method of Duan (1994) for the Merton model by treating the observed equity price as a transformed asset price. I will then show how it can be used to effectively handle the DTD estimation for financial and non-financial firms. There are many plausible reasons that a structural credit risk model prices equity with error. I will thus introduce a methodological advancement by Duan and Fulop (2009) that developed a localized particle filtering scheme for estimating the Merton model with pricing errors.