One of the many uncertainties created by Brexit has concerned its implications for the law relating to civil jurisdiction and the recognition and enforcement of judgments given by the Courts of EU and EFTA member states (and the recognition and enforcement of English or Scottish judgments within the EU and EFTA).
Prior to Brexit, a common set of rules determined the allocation of jurisdiction between the civil courts of the UK and those of other EU and EFTA states. These rules were laid down in the Brussels Regulation (Recast) No. 1215/2012 (for the EU) and the Lugano Convention 2007 (for EFTA member states). Common rules similarly determined when judgments given by the courts of those states would be recognised and enforced in the other EU/EFTA member states. The existence of these rules created a broad measure of certainty as to which court within the EU/EFTA states would have jurisdiction to determine litigation involving parties from more than one such state. They also established that other EU/EFTA states would recognise and enforce judgments that had been given by the court granted jurisdiction under those rules.
EU regulations also provided common rules on the identification of the applicable law to determine claims in both contract and tort (in the form of the Rome I and Rome II regulations).
There is no real reason why any of those rules could not have continued to apply post-Brexit. But there has been considerable uncertainty as to whether they would and similar uncertainty as to what (if any) rules would replace them if they did not continue in effect.