The design of adaptive nonlinear filters has sparked a great interest in the machine learning community. The present paper aims to present some recent developments in nonlinear adaptive filtering. It provides an in-depth analysis of the performance and complexity of a class of kernel filters based on the least-mean-squares algorithm. A key feature that underlies kernel algorithms is that they map the data in a high-dimensional feature space where linear filtering is performed. The arithmetic operations are carried out in the initial space via evaluation of inner products between pairs of input patterns called kernels. The SNR improvement and the convergence speed of kernel-based least-mean-squares filters are evaluated on two types of applications: time series prediction and cardiac artifacts extraction from magnetoencephalographic data.