Abstract: A graph is said to be half-arc-transitive if the automorphism group of the graph acts transitively on the vertex set and the edge set of the graph, but not on the arc set of the graph. In this talk we present results on classification of half-arc-transitive graphs of orders p, 2p, 3p, 4p, pq, 2pq, p^2, p^3, p^4 and 2p^2, where p and q are primes, with an emphasis on tetravalent graphs.