Wat is Gradient descent, line search?

Gradient descent iterates $x_{k+1} = x_k - t_k\nabla f(x_k)$. A line search chooses the step $t_k$ along the descent direction, for instance to satisfy the Wolfe conditions: sufficient decrease, $f(x + td) \le f(x) + c_1t\nabla f(x)^\top d$, and a curvature condition, $|\nabla f(x + td)^\top d| \le c_2|\nabla f(x)^\top d|$, with $0 < c_1 < c_2 < 1$.