This article presents a wide-ranging review of the simulation-based biological fluid dynamic models that have been developed and used in animal swimming and flying. The prominent feature of biological fluid dynamics is the relatively low Reynolds number, e.g. ranging from to for most insects; and, in general, the highly unsteady motion and the geometric variation of the object result in large-scale vortex flow structure. We start by reviewing literature in the areas of fish swimming and insect flight to address the usefulness and the difficulties of the conventional theoretical models, the experimental physical models, and the computational mechanical models. Then we give a detailed description of the methodology of the simulation-based biological fluid dynamics, with a specific focus on three kinds of modeling methods: (1) morphological modeling methods, (2) kinematic modeling methods, and (3) computational fluid dynamic methods. An extended discussion on the verification and validation problem is also presented. Next, we present an overall review on the most representative simulation-based studies in undulatory swimming and in flapping flight over the past decade. Then two case studies, of the tadpole swimming and the hawkmoth hovering analyses, are presented to demonstrate the context for and the feasibility of using simulation-based biological fluid dynamics to understanding swimming and flying mechanisms. Finally, we conclude with comments on the effectiveness of the simulation-based methods, and also on its constraints.