What is algebraic in process theory?

Process theory started in the 1970's with an emphasis on giving an algebraic treatment of its fundamental concepts. In the 1990's, with the rapid introduction of advanced features (data, time, mobility, probability, stochastics), the algebraic line was largely abandoned. I believe that a thorough abstract algebraic treatment adds a degree of mathematical maturity and elegance to the theory. In this note I discuss what is algebraic in process theory, and what is not (yet).