This book looks at the question of extending the reach of the Brussels Ia Regulation to defendants not domiciled in an EU Member State. The Regulation, the centrepiece of the EU framework on civil procedure, is widely recognised as one of the most successful legal instruments on judicial cooperation. To provide a basis for the discussion of its possible extension, this volume takes a closer look at the national rules that currently govern the question of jurisdiction over non-EU defendants in each Member State through 17 national reports. The insights gained from them are summarised in a comparative report and critically discussed in further contributions, which look at the question both from a European and from a wider global perspective. Private international lawyers will be keen to read the findings and conclusions, which will also be of interest to practitioners and policy makers.