Boundary-element methods, also known as panel methods, have been widely used for computations of wave loads and other hydrodynamic characteristics associated with the interactions of offshore structures with waves. In the conventional approach, based on the low-order panel method, the submerged surface of the structure is represented by a large number of small quadrilateral plane elements, and the solution for the velocity potential or source strength is approximated by a constant value on each element. In this paper, we describe two recent developments of the panel method. One is a higher-order method where the submerged surface can be represented exactly, or approximated to a high degree of accuracy by B-splines, and the velocity potential is also approximated by B-splines. This technique, which was first used in the research code HIPAN, has now been extended and implemented in WAMIT. In many cases of practical importance, it is now possible to represent the geometry exactly to avoid the extra work required previously to develop panel input files for each structure. It is also possible to combine the same or different structures which are represented in this manner, to analyze multiple-body hydrodynamic interactions. Also described is the pre-corrected Fast Fourier Transform method (pFFT) which can reduce the computational time and required memory of the low-order method by an order of magnitude. In addition to descriptions of the two methods, several different applications are presented.