Binomial filters are simple and efficient structures based on the binomial coefficients for implementing Gaussian filtering. They do not require multipliers and can therefore be implemented efficiently in programmable hardware. There are many possible variations of the basic binomial filter structure, and they provide a wide range of space-time trade-offs; a number of these designs have been captured in a parametrised form and their features are compared. This technique can be used for multi-dimensional filtering, provided that the filter is separable. The numerical performance of binomial filters, and their implementation using field-programmable devices for an image processing application, are also discussed.