Interference constitutes a major challenge for communication networks operating over a shared medium where availability is imperative. This dissertation studies the problem of designing and analyzing efficient medium access protocols which are robust against strong adversarial jamming. More specifically, four medium access (MAC) protocols (i.e., JADE, ANTIJAM, COMAC, and SINRMAC) which aim to achieve high throughput despite jamming activities under a variety of network and adversary models are presented. We also propose a self-stabilizing leader election protocol, SELECT, that can effectively elect a leader in the network with the existence of a strong adversary. Our protocols can not only deal with internal interference without the exact knowledge on the number of participants in the network, but they are also robust to unintentional or intentional external interference, e.g., due to co-existing networks or jammers. We model the external interference by a powerful adaptive and/or reactive adversary which can jam a (1 − ε)-portion of the time steps, where 0 < ε ≤ 1 is an arbitrary constant. We allow the adversary to be adaptive and to have complete knowledge of the entire protocol history. Moreover, in case the adversary is also reactive, it uses carrier sensing to make informed decisions to disrupt communications. Among the proposed protocols, JADE, ANTIJAM and COMAC are able to achieve Θ(1)-competitive throughput with the presence of the strong adversary; while SINRMAC is the first attempt to apply SINR model (i.e., Signal to Interference plus Noise Ratio), in robust medium access protocols design; the derived principles are also useful to build applications on top of the MAC layer, and we present SELECT, which is an exemplary study for leader election, which is one of the most fundamental tasks in distributed computing.