Time series classification has received great attention over the past decade with a wide range of methods focusing on predictive performance by exploiting various types of temporal features. Nonetheless, little emphasis has been placed on interpretability and explainability. In this paper, we formulate the novel problem of explainable time series tweaking, where, given a time series and an opaque classifier that provides a particular classification decision for the time series, we want to find the changes to be performed to the given time series so that the classifier changes its decision to another class. We show that the problem is NP-hard, and focus on three instantiations of the problem using global and local transformations. In the former case, we investigate the k-nearest neighbor classifier and provide an algorithmic solution to the global time series tweaking problem. In the latter case, we investigate the random shapelet forest classifier and focus on two instantiations of the local time series tweaking problem, which we refer to as reversible and irreversible time series tweaking, and propose two algorithmic solutions for the two problems along with simple optimizations. An extensive experimental evaluation on a variety of real datasets demonstrates the usefulness and effectiveness of our problem formulation and solutions.