Recent developments of the fast multipole method (FMM) will be presented. The first part will consider a black box or kernel independent multipole method, where the user only provides a routine which evaluates the kernel at given points. In many applications, the kernel is not analytically known or is very complicated. Consequently, deriving an FMM from analytical formulas is not always possible or practical. A new black box approach will be presented based on Chebyshev polynomial interpolation and the singular value decomposition of functions. We will compare this algorithm and the analytical FMM in terms of accuracy and run time. We will also consider the important case of periodic boundary conditions and some issues related to the conditional convergence of the sum for certain kernels. If time allows, the second part of the talk will describe a new variant of the FMM for the Helmholtz kernel where a Fourier basis is used instead of spherical harmonics. This reduces significantly the cost of shifting multipole expansions up and down the oct-tree. We will discuss the algorithm, the error analysis and will present some numerical results.