A forward problem in environmental acoustics asks, 'Given the environment, what is the received signal?' High fidelity forward models then allow us to address the inverse problem, 'Given recorded acoustic data, what is the environment?' Solving the forward problem requires a combination of physical understanding, theoretical development, and analytic and numerical modeling. The inverse problem offers many challenges as well, since it may be nonlinear, non-unique, and sensitive to uncertainty in environmental properties and the details of the acoustic data.