How well do we understand string theory? As one indicator can be thought of the degree of our understanding of its spectrum. Yet, other than comprising infinitely many physical states of arbitrarily high spin and mass, what does the string spectrum look like? Traditional methodologies can yield its state content on a level-by-level basis, a straightforward procedure which however becomes cumbersome as the level increases. In this seminar, we will discuss a new, covariant and efficient technology with which entire physical trajectories can be excavated. It is based on the observation that the Virasoro constraints in fact encode the generators of a bigger algebra, that is a symplectic algebra, which commutes with the spacetime Lorentz algebra. This enables constructing trajectories deeper inside the spectrum as clones of simpler ones, upon suitably dressing the latter, depending on the depth of the trajectory we aim to reach.