This paper provides an overview of noise analysis techniques and noise models for radio frequency (RF) circuits and the implication of noise constraints on RF circuit design. In order to accurately account for the circuit nonlinearities, the circuit noise sources are modelled as stochastic processes and the circuit equations are solved with these stochastic processes as inputs, using techniques from stochastic calculus. Noise analysis and modelling techniques are presented for both autonomous (oscillatory) and non-autonomous circuits. Using these models, noise analysis of a phase feedback system (phase-locked loop) is also presented. Additionally, design techniques for minimizing noise in these circuits which are based on these analyses are also presented.