A living systematic review (LSR) should keep the review current as new research evidence emerges. Any meta-analyses included in the review will also need updating as new material is identified. If the aim of the review is solely to present the best current evidence standard meta-analysis may be sufficient, provided reviewers are aware that results may change at later updates. If the review is used in a decision-making context, more caution may be needed. When using standard meta-analysis methods, the chance of incorrectly concluding that any updated meta-analysis is statistically significant when there is no effect (the type I error) increases rapidly as more updates are performed. Inaccurate estimation of any heterogeneity across studies may also lead to inappropriate conclusions. This paper considers four methods to avoid some of these statistical problems when updating meta-analyses: two methods, that is, law of the iterated logarithm and the Shuster method control primarily for inflation of type I error and two other methods, that is, trial sequential analysis and sequential meta-analysis control for type I and II errors (failing to detect a genuine effect) and take account of heterogeneity. This paper compares the methods and considers how they could be applied to LSRs.