This document is the thesis submitted by Oscar del Río Herrero for the degree of Doctor of Philosophy at Universitat Ramon Llull in Barcelona, Spain in 2015. The thesis proposes three novel random access schemes for satellite communications: Contention Resolution Diversity Slotted Aloha (CRDSA), Asynchronous Contention Resolution Diversity Aloha (ACRDA), and Enhanced Spread Spectrum Aloha (E-SSA). CRDSA uses strong error correction codes and successive interference cancellation to achieve high throughput for slotted systems. ACRDA extends this technique to unslotted systems using spreading sequences. E-SSA applies similar concepts to spread spectrum systems. The performance of the schemes is