<p>As artificial intelligence and machine learning (ML) have grown in popularity over the past few decades, they are now being applied to a multitude of fields. While making decisions in this domain, the limitations of bias and fairness have become very important issues for researchers and engineers. As a result, it is crucial to be concerned about the potential harmfulness of data and algorithms while choosing them for an AI application. In this view, this paper introduces a review of the definition of bias with a few real-life examples in ML, different types of bias, methods to mitigate bias, fairness in ML, some tools to detect bias in ML algorithms, metrics for fairness measurement, and some typical datasets used by researchers to study the fairness of ML algorithms. The main contribution of this paper is to present the concepts of bias and fairness, tools, datasets, and metrics for technical and non-technical people such as philosophers, policymakers, lawyers, and social scientists for further related study and research in their domain of interest relevant to ML algorithms. Some future research directions in the area of fairness in ML algorithms are highlighted.</p>