This thesis contributes to knowledge by describing two novel methods to calculate 3D blood velocity and flow within the heart using 3D colour Doppler images. The principal goal of both methods was to overcome the main limitation of Doppler systems which is that the Doppler effect only measures one component of the velocity (parallel to the beam direction). For that reason, measured velocity and calculated flow depend on the angle between the beam direction and the flow. The first method was developed to reconstruct 3D intracardiac velocity vector fields. This is the first time that such vector fields have been obtained from 3D colour Doppler images. The novelty of the proposal lies not only in the 3D velocity reconstruction, but also 1) a new noise model for colour Doppler images was proposed which improves the realism of simulation studies, 2) an efficient patch-wise implementation was introduced and 3) ventricle wall motion was used to enable full ventricular coverage. Based on simulations minimum acquisition requirements for accurate reconstruction were established. These requirements were: view angles over 20 degrees and noise below 10% of the Doppler maximum velocity. The method was tested on healthy volunteers and on paediatric patients and an accuracy of 15% compared to flow Magnetic Resonance Imaging (MRI) was obtained, when acquisition and data conditions were close to the optimum range. The second method proposes an algorithm to calculate angle-independent flow rates through surfaces within the heart and vessels. Built on the Gauss’s theorem, this method enables to increase coverage beyond the Field of View (FoV) of individual colour Doppler images by combining images acquired from multiple views. The method was validated in patients with Hypoplastic Left Heart Syndrome. Results were compared with the current clinical gold standard measurement of flow MRI, agreeing on flow values and volumes to less than 10%. The novel methods proposed in this thesis have shown encouraging results using volunteer and patient data. I hope that the methods proposed will in the future be able to offer advanced flow measurements using echo. The ability to improve the information available from echo imaging, due to its ease of use and cost effective nature, has the potential for widespread improvements in clinical care.