The inherent non-stationarity of time series in practical applications poses significant challenges for accurate forecasting. This paper tackles the concept drift problem where the underlying distribution or environment of time series changes. To better describe the characteristics and effectively model concept drifts, we first classify them into macro-drift (stable, long-term changes) and micro-drift (sudden, short-term fluctuations). Next, we propose a unified meta-learning framework called LEAF (Learning to Extrapolate and Adjust for Forecasting), where an extrapolation module is first introduced to track and extrapolate the prediction model in latent space considering macro-drift, and then an adjustment module incorporates meta-learnable surrogate loss to capture sample-specific micro-drift patterns. LEAF’s dual-stage approach effectively addresses diverse concept drifts and is model-agnostic which can be compatible with any deep prediction model. We further provide theoretical analysis to justify why the proposed framework can handle macro-drift and micro-drift. To facilitate further research in this field, we release three electric load time series datasets collected from real-world scenarios, exhibiting diverse and typical concept drifts. Extensive experiments on multiple datasets demonstrate the effectiveness of LEAF.