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The paper is a brief review on the existence and basic properties of static, spherically symmetric regular black hole solutions of general relativity, where the source of gravity is represented by nonlinear electromagnetic fields with the Lagrangian function $L$ depending on the single invariant $f = F_{\mu\nu}F^{\mu\nu}$ or on two variables: either $L(f, h)$, where $h = {^*}F_{\mu\nu} F^{\mu\nu}$, where ${^*}F_{\mu\nu}$ is the Hodge dual of $F_{\mu\nu}$, or $L(f, J)$, where $J = F_{\mu\nu}F^{\nu\rho} F_{\rho\sigma} F^{\sigma\mu}$.
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