Data extracted from social networks like Twitter are increasingly being used to build applications and services that mine and summarize public reactions to events, such as traffic monitoring platforms, identification of epidemic outbreaks, and public perception about people and brands. However, such services are vulnerable to attacks from socialbots $-$ automated accounts that mimic real users $-$ seeking to tamper statistics by posting messages generated automatically and interacting with legitimate users. Potentially, if created in large scale, socialbots could be used to bias or even invalidate many existing services, by infiltrating the social networks and acquiring trust of other users with time. This study aims at understanding infiltration strategies of socialbots in the Twitter microblogging platform. To this end, we create 120 socialbot accounts with different characteristics and strategies (e.g., gender specified in the profile, how active they are, the method used to generate their tweets, and the group of users they interact with), and investigate the extent to which these bots are able to infiltrate the Twitter social network. Our results show that even socialbots employing simple automated mechanisms are able to successfully infiltrate the network. Additionally, using a $2^k$ factorial design, we quantify infiltration effectiveness of different bot strategies. Our analysis unveils findings that are key for the design of detection and counter measurements approaches.