In insurance industry, the financial stability of insurance companies represents an issue of vital importance. In order to maintain the financial stability and meet minimum regulatory requirements, actuaries apply actuarial modeling. Modeling has been at the center of actuarial science and of all the sciences from the beginning of their journey. In insurance industry, actuarial modeling creates a framework that allows actuaries to identify, understand, quantify and manage a wide range of risks, especially actuarial risks. Actuarial modeling uses as key instruments actuarial models which represent a simplification of a real system, facilitating understanding and prediction of the real system. Therefore, these models are designed to be appropriate with the essential principles of actuarial science. In actuarial modeling progress is marked by breaking existent barriers and developing and incorporating new types of actuarial models.