The exponential increase in dependencies between the cyber and physical world leads to an enormous amount of data which must be efficiently processed and stored. Therefore, computing paradigms are evolving towards machine learning (ML)-based systems because of their ability to efficiently and accurately process the enormous amount of data. Although ML-based solutions address the efficient computing requirements of big data, they introduce security vulnerabilities into the systems, which cannot be addressed by traditional monitoring-based security measures. Therefore, this paper first presents a brief overview of various security threats in machine learning, their respective threat models and associated research challenges to develop robust security measures. To illustrate the security vulnerabilities of ML during training, inferencing and hardware implementation, we demonstrate some key security threats on ML using LeNet and VGGNet for MNIST and German Traffic Sign Recognition Benchmarks (GTSRB). Moreover, based on the security analysis of ML-training, we also propose an attack that has very less impact on the inference accuracy. Towards the end, we highlight the associated research challenges in developing security measures and provide a brief overview of the techniques used to mitigate such security threats.