Summary: This paper discusses the importance and relevance of direct continuous-time system identification and how this relates to the solution for model identification problems in practical applications. It first gives a tutorial introduction to the main aspects of one of the most successful existing approaches for directly identifying continuous-time models of dynamical systems from sampled input-output data. Compared with traditional discrete-time model identification methods, the direct continuous-time approaches have some notable advantages that make them more useful in many practical applications. For instance, continuous-time models are more intuitive to control scientists and engineers in their every-day practice and the related estimation methods are particularly well suited to handle rapidly or irregularly sampled data situations. The second part of the paper describes further recent developments of this reliable estimation technique, including its extension to handle coloured measurement noise situations, time-delay system identification, frequency-domain identification, non-uniformly sampled data, closed-loop and nonlinear model identification. It also discusses the software tools available and illustrates their advantages via simulated and real data examples.