Abstract: Recently, there have been many advances in using quantum computers for machine learning tasks. Among these include using the quantum computer to encode data in a quantum state using nonlinear feature maps. One way of using this nonlinear feature map is to estimate the inner product, or kernel, of two data points. The value of the kernel can then be used in classical machine learning tasks, such as classification using support vector machines. Here, we discuss some aspects of quantum kernels and demonstrate their usefulness in a variety of machine learning tasks, including classification, regression, and reinforcement learning, all using Gaussian processes. We show how using quantum kernels inspired by classical kernels, such as the radial basis function (or Gaussian) kernel, can lead to interesting quantum kernels with additional learning ability. We also discuss how quantum computers might offer advantage for these tasks, once quantum devices which are classically intractable to simulate, are available.