We present recent developments on post-production calibration of analog and radio frequency (RF) integrated circuits (ICs) mainly focusing on on-chip solutions. Specifically, we summarize the state-of-the-art on both direct and statistical calibration techniques. The latter typically employ on-die sensors, which estimate the circuit under test (CUT) performances and tuning knobs, which along with machine learning-based methods are capable of calibrating the CUT. Existing sensors, tuning knobs and machine learning-based implementations are discussed and their limitations are outlined. Lastly, a fully integrated new architecture for on-chip calibration of a low-noise amplifier (LNA) through the use of an analog neural network is introduced.