DSP chips are optimized for the repeated multiply-add operations that audio processing requires. They are found in: audio interfaces (for zero-latency monitoring effects), active studio monitors (for crossover and room correction), wireless headphones (for ANC and codec processing), and guitar modelers.
Software DSP (running on your computer's CPU as VST/AU plugins) has largely replaced hardware DSP for studio use. Hardware DSP remains relevant for live sound (where reliability and zero-latency are critical) and UAD's Apollo interfaces (which run UAD plugins on onboard SHARC DSP chips).