A concise account is given about Monte Carlo (MC) simulation techniques for homogeneous and inhomogeneous systems of electrolyte solutions at concentrations characteristic of biological situations. While the techniques are quite general, the focus here is on reduced models of ion channels where the electrolyte is modeled in the implicit solvent framework, while the channel and the membrane are modeled using minimal structural information. The ion channels under consideration are the L-type calcium channel (present in muscle cell membranes) and the ryanodine receptor calcium release channel (present in the membrane of the sarcoplasmic reticulum). Although MC simulations are known to be appropriate to simulate equilibrium systems, these examples show how to use MC techniques to simulate nonequilibrium ionic transport. The Local Equilibrium Monte Carlo method is shown to be especially useful to simulate globally nonequilibrium systems by coupling MC to the Nernst-Planck transport equation.