In the halls of Lambeth Palace, where the Archbishop of Canterbury lives, there are portraits of an unbroken succession of Archbishops from St Augustine to Justin Welby. (is he the current one?) Some Anglicans consider this Apostolic Succession. Others do not care.
Catholics, following the teaching of Leo XIII, do not believe that this succession of archbishops is a succesion from the Apostles. That is, an unbroken line of bishops is no longer the definition of Apostolic Succession. Now it has to be defined in a somewhat elusive manner, as succession in fidelity to something that cannot be defined very well.
Some Lutherans also claim Apostolic Succession. Scandinavian Lutherans have an unbroken line of bishops. (Though Rome denies it) other Lutherans believe priests have the fullness of Orders as bishops do, so the succesion of ordained Lutherans is an Apostolic Succession. This is true, for them, only if the Gospel is preached and sacraments are administered properly.
Catholic teaching says these bishops are not bishops, these pastors are not priests. Not everyone agrees.