Input-to-state stability (ISS) is a concept introduced to analyze the stability of nonlinear dynamical systems under external inputs. ISS not only ensures that the system behaves stable in the absence of inputs, but also maintains this nominal behavior with deviations proportional to the input magnitude. From another perspective, small inputs lead to small steady-state errors for such systems. An important extension of ISS is the integral ISS (iISS), which relates the norm of the system trajectories to the energy of the input rather than the input amplitude. In this talk, we will first introduce the concepts and tools of ISS/iISS. We will then discuss recent developments related to these concepts in time-delay systems, emphasizing their differences from finite-dimensional systems. Next, we present new Lyapunov-Krasovskii conditions for Strong iISS, a stability concept that guarantees not only iISS but also ISS under inputs whose amplitudes are below a certain threshold. Finally, we discuss some open problems in this research area.