In the last few years, wireless sensor networks (WSNs) have become a very actively researched area. The impetus for this spurt of interest were developments in wireless technologies and low-cost VLSI, that made it possible to build inexpensive sensors and actuators. Each such device has limited computational power, memory and energy supply. Nevertheless, because of the low cost, such devices can be deployed in large numbers, and can thereafter form a sensor network. Usually, one or more base stations are also present which act as sink nodes. When sensors are deployed in hostile environments, security becomes an integral part for such type of networks. A first step in this direction is to provide secure communication between any two nodes and between a node and the base station. Since the public key cryptographic techniques are computationally expensive for resource constrained sensors, one need to rely on symmetric key cryptography for secure communication. The distribution and management of cryptographic keys poses a unique challenge in sensor networks. One requires efficient key distribution algorithms for such type of networks. In this thesis, we address the problem of secure path key establishment in wireless sensor networks. We first propose a pairwise key distribution algorithm for probabilistic schemes. Inspired by the recent proxy-based schemes, we introduce a friend-based scheme for establishing pairwise keys securely. We show that the chances of finding friends in a neighbourhood are considerably more than that of finding proxies, leading to lower communication overhead. Further, we prove that the friend-based scheme performs better than the proxy-based scheme both in terms of resilience against node capture as well as in energy consumption for pairwise key establishment. A recent study has shown that the advantages of the probabilistic approach over the deterministic approach, are not as much as people have believed. Thus, we focus our attention on deterministic schemes in which we first discuss why one cannot use the conventional security measure for determining the resilience of a key distribution scheme in case of schemes in which nodes share more than one key. Then, we propose a new and a more general security metric for measuring the resilience of a key distribution scheme in wireless sensor networks. Further, we present a polynomial-based scheme and a novel complete connectivity scheme for distributing keys to sensors and show an analytical comparison, in terms of security and connectivity, between the schemes. Motivated by the schemes, we derive general expressions for the new security measure and the connectivity. A number of conclusions are made using these general expressions. Then, we conclude our work with a number of future directions that can be followed with this piece of work.