Genomic data holds salient information about the characteristics of a living organism. Throughout the last decade, pinnacle developments have given us more accurate and inexpensive methods to retrieve genome sequences of human beings. However, with the advancement of genomic research, there is a growing privacy concern regarding the collection, storage, and analysis of such sensitive data. Recent research results show that given some background information, it is possible for an adversary to re-identify an individual from any genomic dataset. In this thesis, we examine various data sharing models and study the potential privacy attacks in different real-life data sharing scenarios. We then propose appropriate privacy-preserving solutions using cryptographic and statistical techniques. Experimental results show that our proposed solutions are scalable and can guarantee both utility and privacy of the genomic data.