Interactively simulating visual appearance of natural objects under natural illumination is a fundamental problem in computer graphics. 3D computer games, geometry modeling, training and simulation, electronic commerce, visualization, lighting design, digital libraries, geographical information systems, economic and medical image processing are typical candidate applications. Recent advances in graphics hardware have enabled real-time rasterization of complex scenes under artificial lighting environment. Meanwhile, pre-computation based soft shadow algorithms are proven effective under low-frequency lighting environment. Under the most practical yet popular all-frequency natural lighting environment, however, real-time rendering of dynamic scenes still remains a challenging problem. In this dissertation, we propose a systematic approach to render dynamic glossy objects under the general all-frequency lighting environment. In our framework, lighting integration is reduced to two rather basic mathematical operations, efficiently computing multi-function product and product integral. The main contribution of our work is a novel mathematical representation and analysis of multi-function product and product integral in the wavelet domain. We show that, multi-function product integral in the primal is equivalent to summation of the product of basis coefficients and integral coefficients. In the dissertation, we give a novel Generalized Haar Integral Coefficient Theorem. We also present a set of efficient algorithms to compute multi-function product and product integral. In the dissertation, we demonstrate practical applications of these algorithms in the interactive rendering of dynamic glossy objects under distant time-variant all-frequency environment lighting with arbitrary view conditions. At each vertex, the shading integral is formulated as the product integral of multiple operand functions. By approximating operand functions in the wavelet domain, we demonstrate rendering dynamic glossy scenes interactively, which is orders of magnitude faster than previous work. As an important enhancement to the popular Pre-computation Based Radiance Transfer (PRT) approach, we present a novel Just-in-time Radiance Transfer (JRT) technique, and demonstrate its application in real-time realistic rendering of dynamic all-frequency shadows under general lighting environment. Our work is a significant step towards real-time rendering of arbitrary scenes under general lighting environment. It is also of great importance to general numerical analysis and signal processing.