This chapter reveals a definition of extremal (maxima) random sequences and stochastic processes. Extremal sequences are the usual sequences of maxima. It can be obtained as stochastic processes of independent extremes with extremal margins. Extremal sequences and processes (distribution and properties), limiting characterizations, second order properties of extremal processes, jumps of an extremal process, logarithmization of time and the ergodic theorem for extremal processes, parameterization of extremal processes and statistics for extremal sequences and processes are discussed with explanatory examples.