Two-timescale learning algorithms are widely used in game theory and multi-objective optimization to achieve better convergence performance using distinct update rates for two interdependent processes. In this talk, I will discuss the convergence properties of two specific types of algorithms. The first is the two-timescale gradient descent-ascent algorithm, designed to find Nash equilibria in min-max games. The second is a unified two-timescale Q-learning algorithm, which is capable of solving both mean field game and mean field control problems by simply adjusting its learning rate ratio for mean field distribution and Q-functions. I will present several convergence results for these algorithms, focusing on the impact of learning rate ratios. Our analysis draws tools such as Lyapunov functions and couplings from partial differential equations and stochastic analysis.