This paper surveys our current state of knowledge (and ignorance) on the use of hidden sorted algebra as a foundation for the object paradigm. Our main goal is to support equational reasoning about properties of concurrent systems of objects, because of its simple and ecient mechanisation. We show how equational speci cations can describe objects, inheritance and modules; our treatment of the latter topic emphasises the importance of reuse, and the r^ole of the so-called Satisfaction Condition. We then consider how to prove things about objects, how to unify the object and logic paradigms by using logical variables that range over objects, and how to connect objects into concurrent systems.