We study the problem of computing isochrones in road networks, where the objective is to identify the region that is reachable from a given source within a certain amount of time. While there is a wide range of practical applications for this problem (e.g., reachability analyses, geomarketing, visualizing the cruising range of a vehicle), there has been little research on fast computation of isochrones on large, realistic inputs. In this work, we formalize the notion of isochrones in road networks and present a basic approach for the resulting problem based on Dijkstra's algorithm. Moreover, we consider several speedup techniques that are based on previous approaches for one-to-many shortest path computation (or similar scenarios). In contrast to such related problems, the set of targets is not part of the input when computing isochrones. We extend known Multilevel Dijkstra techniques (such as CRP) to the isochrone scenario, adapting a previous technique called isoGRASP to our problem setting (thereby, enabling faster queries). Moreover, we introduce a family of algorithms based on (single-level) graph partitions, following different strategies to exploit the efficient access patterns of PHAST, a well-known approach towards one-to-all queries. Our experimental study reveals that all speedup techniques allow fast isochrone computation on input graphs at continental scale, while providing different tradeoffs between preprocessing effort, space consumption, and query performance. Finally, we demonstrate that all techniques scale well when run in parallel, decreasing query times to a few milliseconds (orders of magnitude faster than the basic approach) and enabling even interactive applications.