Conversational Task Assistants (CTAs) are conversational agents whose goal is to help humans perform real-world tasks. CTAs can help in exploring available tasks, answering task-specific questions and guiding users through step-by-step instructions. In this work, we present Wizard of Tasks, the first corpus of such conversations in two domains: Cooking and Home Improvement. We crowd-sourced a total of 549 conversations (18,077 utterances) with an asynchronous Wizard-of-Oz setup, relying on recipes from WholeFoods Market for the cooking domain, and WikiHow articles for the home improvement domain. We present a detailed data analysis and show that the collected data can be a valuable and challenging resource for CTAs in two tasks: Intent Classification (IC) and Abstractive Question Answering (AQA). While on IC we acquired a high performing model (>85% F1), on AQA the performance is far from being satisfactory (~27% BertScore-F1), suggesting that more work is needed to solve the task of low-resource AQA.