Fractal geometry, developed by B. Mandelbrot, has provided new key concepts necessary to the understanding and quantification of some aspects of pattern and shape randomness, irregularity, complexity and self-similarity. In the field of microscopy, fractals have profound implications in relation to the effects of magnification and scaling on morphology and to the methodological approaches necessary to measure self-similar structures. In this article are reviewed the fundamental concepts on which fractal geometry is based, their relevance to the microscopy field as well as a number of technical details that can help improving the robustness of morphological analyses when applied to microscopy problems.