This paper presents a focused and comprehensive literature survey on the use of machine learning (ML) in antenna design and optimization. An overview of the conventional computational electromagnetics and numerical methods used to gain physical insight into the design of the antennas is first presented. The major aspects of ML are then presented, with a study of its different learning categories and frameworks. An overview and mathematical briefing of regression models built with ML algorithms is then illustrated, with a focus on those applied in antenna synthesis and analysis. An in-depth overview on the different research papers discussing the design and optimization of antennas using ML is then reported, covering the different techniques and algorithms applied to generate antenna parameters based on desired radiation characteristics and other antenna specifications. Various investigated antennas are sorted based on antenna type and configuration to assist the readers who wish to work with a specific type of antennas using ML.