Hilbert space frames were introduced by Duffin and Schaeffer while studying deep questions in non-harmonic Fourier series. Today they have broad application to problems in pure mathematics, applied mathematics, engineering, medicine and more. The present research is divided into two main areas: frame theoretic results and applications of frames. In particular, the beginning half develops a detailed theory of the distribution of frame coefficients. After this, the first systematic study of integer frames is included. Finally, the research is concerned with the application of frames to the area of signal reconstruction. In particular, phase retrieval by subspace components and norm retrieval are discussed.