Upper-level Rossby wave packets (RWPs) are one of the key drivers of surface weather. RWPs can lead to extreme surface weather events. However, extreme impacts can also arise from long spells of persistent weather. Recurrence of synoptic-scale RWPs, termed RRWPs, where RWPs recur in the same phase over a short period, can also lead to persistent weather. The importance of RRWPs has only been identified recently. This thesis aims to explore the role of RRWPs in modulating persistent weather events and discover the atmospheric processes driving RRWPs. First, the thesis quantifies the significance of RRWPs for dry and wet spells across the globe. Persistent dry spells can lead to droughts, make heatwaves more extreme, and increase the risk of forest fires. The thesis finds that RRWPs are significantly associated with longer dry and wet spells across the globe. The case studies further demonstrate the role of RRWPs during episodes of dry and wet spells, respectively. Next, the thesis explores the role of RRWPs for hot spells in the SH. For the hot spells, RRWPs are significantly associated with longer hot spells over several regions, including south-eastern Australia (SEA), a region that has seen increasingly extreme heatwaves in recent decades. Motivated by that, the importance of RRWPs for the set of most persistent and extreme SEA heatwaves is explored further. The role of RRWPs during SEA heatwaves is demonstrated by two case studies of 2004 and 2009 SEA heatwaves, where RRWPs help to build recurrent ridges over SEA. Furthermore, days with RRWP conditions over SEA are associated with an increased probability of SEA heatwaves. Given the vital role of RRWPs for SEA heatwaves, the thesis sets out to find the association of RRWPs with other atmospheric drivers of persistent weather, namely, atmospheric blocks and quasi-resonance amplification (QRA). QRA conditions were also detected during some episodes of the most persistent and extreme SEA heatwaves. We find that RRWPs and QRA are closely associated in the SH, with 40% of QRA days also featuring RRWP conditions. We study their close association with upper-level composite maps and discuss the similarities and differences in the algorithm used to identify them. For the link of RRWPs and QRA with blocks in SH, we find an insignificant increase in the median area of blocks for days with RRWP than without and a slight decrease for QRA days than non-QRA days. We also find substantial differences in the spatial distribution of blocks between QRA days and RRWP days. Motivated by the vital role of the RRWPs, the latter part of this thesis investigates the causal drivers of RRWPs in the North Atlantic for the winter and summer seasons. RRWP episodes for summer and winter are used to identify possible causal drivers of RRWPs, whose relevance is subsequently examined in a causal network (CN) framework. The CNs reveal that local changes over the Atlantic in atmospheric blocking and low wavenumber background flow primarily drive RRWPs for both seasons. RRWPs also have feedback on background flow and blocks. In winter, tropical forcing has an indirect link with RRWPs, which drives background flow changes over the Pacific, and subsequently modifies background flow over the Atlantic. In summer, a direct link from background flow over the Pacific to RRWPs exists. CNs also reveal a robust link from extratropics to tropics in the summer, where background flow over North Atlantic drives changes in the background flow over the Pacific.