Most mainstream programming languages support finalizers and weak references. In spite of that, these abstractions are still modestly known by programmers in general. Even among language designers there seems to be no common view on how to define their semantics, and language implementations certainly reflect that. In this thesis we explore the concepts of finalizer and weak reference by discussing several important issues that, as far as we know, have not been explored by other authors. After presenting a survey on how finalizers and weak references are supported by actual programming languages, we thoroughly examine their semantics and discuss alternative implementation strategies. We also use an operational approach to develop a formal model for reasoning about garbage collection and its interaction with client programs. By explicitly representing low-level details, such as heap memory and its addresses, we were able to clearly specify memory management actions, and prove several important memory-related language invariants. Using this model we describe a formal semantics for finalizers and weak references, exploring some of its many subtleties. We believe that the topics covered here can serve as a relevant reference for further investigations, and also help to guide actual implementations.