Dual model amplitudes are weakly coupled (tree-level) amplitudes involving the exchange of infinitely-many higher spin states. They are the staple of tree-level string theory, with the Veneziano and Virasoro-Shapiro amplitudes being their most famous representatives, but they also appear in the large N limit of gauge theories as QCD, which becomes a weakly coupled theory of baryons and glueballs in the limit where the number of colors goes to infinity. While they were first discovered in the 60s in the context of the Hadronic S-matrix Bootstrap program and subsequently led to the discovery of String Theory and its proposal as a theory for Quantum Gravity, there is still a lot to learn about their basic properties and this is the central theme of this thesis. Unveiling their secrets would shed light on the structures of both String Theory and QCD via its large N limit. The main body of the thesis is divided in two parts. In the first one I study this class of amplitudes from a bootstrap perspective, namely using the requirements of analyticity, crossing symmetry and unitarity to constrain, or in some cases even derive, dual model amplitudes. I start by an introduction to the S-matrix bootstrap and its application to tree-level amplitudes. Then, I apply this framework to study the Coon amplitude, a solution to the dual model amplitude bootstrap constraints known since the late 60s but whose main properties remained largely unknown. I describe our new results concerning their unitarity properties and critical dimension, and introduce a generalization of the method used to originally derive the Coon amplitude. I continue by an elementary introduction to Regge theory, and I use it as a tool to study dual model amplitudes. In particular, I use techniques from this toolkit to show that dual model amplitudes require infinitely many Regge trajectories to be consistent. Finally, I end the first part by introducing a numerical bootstrap method based on Regge theory to obtain solutions to the bootstrap constraints on dual amplitudes. I make use of this method to obtain for the first time consistent dual model amplitudes with bending Regge trajectories, a feature expected from the ones corresponding to large N gauge theories. The second part of this thesis is devoted to the study of three-point amplitudes between physical 1-particle states of arbitrary mass and spin in String Theory, a basic object missing in the literature that has various applications ranging from building higher point amplitudes of arbitrary external states to exploring high energy string scattering and its connection to black holes. A crucial part of the problem is imposing the physical state condition, and we do so by using the lightcone gauge formalism to restrict to the physical Hilbert space at the cost of manifest Lorentz invariance. After a short introduction on the lightcone quantization of String Theory, I present our novel method to build full SO(25) 1-particle states from lightcone gauge oscillators, and I show how to bootstrap full trajectories of physical states. In the following chapter I explain the method to compute scattering amplitudes in this formalism and use it to compute three-point amplitudes between infinite classes of 1-particle states, and show how to covariantize the resulting lightcone gauge amplitudes. This part is ended with a discussion on the application of these amplitudes to the study of black holes in String Theory. The thesis concludes with an overall discussion of the results presented as well as of future research directions.