Gradient descent is a widely used optimization algorithm in machine learning and deep learning that iteratively adjusts model parameters to minimize a cost function. It operates by moving parameters in the opposite direction of the gradient. There are three main variants: batch gradient descent, which uses the whole training set; stochastic gradient descent (SGD), which uses individual training examples; and mini-batch gradient descent, which uses subsets of the training data. Challenges include choosing the learning rate and avoiding local minima or saddle points. Optimization algorithms like Momentum, Nesterov accelerated gradient, Adagrad, Adadelta, RMSprop, Adam, AdaMax, and Nadam address these issues. Additional techniques such as shuffling, curriculum learning, batch normalization, early stopping, and gradient noise can improve performance.

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