This paper provides a detailed elaboration and assessment of the most common domain decomposition methods for their application in isogeometric analysis. The methods comprise a penalty approach, Lagrange multiplier methods, and a Nitsche-type method. For the Nitsche method, a new stabilized formulation is developed in the context of isogeometric analysis to guarantee coercivity. All these methods are investigated on problems of linear elasticity and eigenfrequency analysis in 2D. In particular, focus is put on non-uniform rational B-spline patches which join nonconformingly along their common interface. Thus, the application of isogeometric analysis is extended to multi-patches, which can have an arbitrary parametrization on the adjacent edges. Moreover, it has been shown that the unique properties provided by isogeometric analysis, that is, high-order functions and smoothness across the element boundaries, carry over for the analysis of multiple domains. Copyright © 2013 John Wiley & Sons, Ltd.