Are there other filter models besides IIR and FIR for processing digital signals?
FIR and IIR filters are discrete-time linear time-invariant (LTI) filters. There are also (linear) time-varying systems, which could be implemented just like FIR or IIR filters, but with time-varying coefficients. Audio effects like chorus, flanger, or phaser are time-varying filters.

Of course there are also non-linear filters, the most well-known of which is probably the median filter, which is very useful for removing impulsive noise. Many different types of non-linear filters are used in image processing.

Note that none of the above mentioned filters can be characterized by their impulse response or, equivalently, by their frequency response. This is only possible for LTI systems.