This paper gives an overview of the development of Mixed-Integer Nonlinear Programming (MINLP) and Generalized Disjunctive Programming (GDP) over the past fifty years. We cover key methods, algorithms, and techniques for solving MINLPs and GDPs, focusing on both the modeling framework and solution techniques. We provide historical perspectives, highlight the key features and major challenges, and aim to give an in-depth introduction to the fields. We also discuss some future research directions. The paper is aimed at readers who are familiar with Mixed-Integer Linear Programming but are not experts on MINLP or GDP.