Determining the chaotic or regular nature of orbits of dynamical systems is a fundamental problem of nonlinear dynamics, having applications to various scientific fields. The most employed method for distinguishing between regular and chaotic behavior is the evaluation of the maximum Lyapunov exponent (MLE), because if the MLE>0 the orbit is chaotic. The main problem of using this chaos indicator is that its numerical evaluation may take a long -and not known a priori- amount of time to provide a reliable estimation of the MLE’s actual value. In this talk we will focus our attention on two very efficient methods of chaos detection: the Smaller (SALI) and the Generalized (GALI) Alignment Index techniques. We will first recall the definitions of the SALI and the GALI and will briefly discuss the behavior of these indices for conservative Hamiltonian systems and area-preserving symplectic maps. Then, we will explain how one can use these methods to investigate the dynamics of time-dependent dynamical systems, and we will discuss the applicability of these indicators to dissipative systems. Furthermore, we will present some recently introduced methods to estimate the chaoticity of orbits in conservative dynamical systems from computations of Lagrangian descriptors on short time scales.