In a separable Hilbert space L(H,K), two frames {fi}i I and {gi}i I are said to be woven if there are constants 0 < A ≤ B so that for every σ I, {fi}i σ {gi}i σc forms a frame for L(H,K) with the universal bounds A,B. This paper provides methods of constructing woven frames. In particular, bounded linear operators are used to create woven frames from a given frame. Several examples are discussed to validate the results. Moreover, the notion of woven frame sequences is introduced and characterized.