Parallel processing architectures allow for simultaneous computation across multiple processing elements. There are four main types of parallel architectures: single instruction single data (SISD), single instruction multiple data (SIMD), multiple instruction single data (MISD), and multiple instruction multiple data (MIMD). MIMD systems are the most common and can have either shared or distributed memory. Effective parallel programming requires approaches like message passing or shared memory models to facilitate communication between processing elements.