We introduce and review a number of topics drawn from the theories of random processes and random systems. In particular we address the following subjects: random walks in continuous spaces and on lattices; continuum limits of random walks and stable distributions; master equations, generalized master equations and continuous-time random walks; self-avoiding walks on lattices; percolation theory; steady-state and transient transport in random lattices; and diffusion and conduction in heterogeneous continua.