This habilitation manuscript describes the main results that I have obtained in the past eight years on the topic of the timing predictability of real-time systems in the presence of parallelism. From a general perspective, the addressed problem is that of considering the temporal impact on the Worst-Case Execution Time (WCET) of a system composed of multiple parallel software components that compete for the access to a shared sequential hardware component. The manuscript considers this problem at two different complexity levels. First, at instruction level, the problem translates into so-called timing anomalies, which preclude the efficient and safe computation of WCETs. In order to overcome this difficulty, we developed the MINOTAuR core: a timing anomaly-free variant of the CVA6 riscv core. At task system-level, we studied how using a multi-phase representation of the execution of tasks that follows more closely their memory access profile than the previous state-of-the-art representations could be used in order to improve the precision of the inter-core interference analysis in multi-core processors, the reducing significantly the pessimism of the approach. We detail the Time Interest Points framework that allows to derive a multi-phase representation of a task, as well as a series of heuristics to perform the static scheduling of multi-phase tasks in order to reduce the impact of the interference in the system. Finally we provide a set of correctness criteria that guarantee the safe implementation of a set of multi-phase tasks. The manuscript provides the major results on these topics as well as detailed research perspectives for the years to come.