Design of small broadband, multiband and high-directivity microstrip patch antennas (MPAs) is a challenging task for the antenna research community since the classical MPAs do not perform well enough to be used in the real world applications. In this sense, various performance improvement techniques such as stacked patches, air gaps, compact meandering geometries, fractal-shapes and shorting pins are applied to design improved MPAs. Use of bio-inspired algorithms along with these techniques is trending due to their capability of manipulating antenna parameters to achieve optimized performance. Literature presents use of bio-inspired algorithms such as Genetic algorithms (GA), Particle swarm optimization (PSO), Differential evolution (DE), Invasive weed optimization (IWO), Wind driven optimization (WDO) and Ant colony optimization (ACO) on MPAs for performance enhancement. This paper begins with an introduction to MPAs followed by an analysis of the performance improvement techniques. Evolution of bio-inspired algorithms and their applications in the field of MPAs are also presented. Based on the compilation of studies, importance of applying multi-objective bio-inspired algorithms for simultaneous optimization of multiple antenna parameters is emphasized. Further, research voids in the field are revealed and direction is shown to design compact multifunctional MPAs.