Existing works on grant-free access, proposed to support massive machine-type communication (mMTC) for the Internet of things (IoT), mainly concentrate on narrow band systems under flat fading. However, little is known about massive grant-free access for wideband systems under frequency-selective fading. This paper investigates massive grant-free access in a wideband system under frequency-selective fading. First, we present an orthogonal frequency division multiplexing (OFDM)-based massive grant-free access scheme. Then, we propose two different but equivalent models for the received pilot signal, which are essential for designing various device activity detection and channel estimation methods for OFDM-based massive grant-free access. One directly models the received signal for actual devices, whereas the other can be interpreted as a signal model for virtual devices. Next, we investigate statistical device activity detection under frequency-selective Rayleigh fading based on the two signal models. We first model device activities as unknown deterministic quantities and propose three maximum likelihood (ML) estimation-based device activity detection methods with different detection accuracies and computation times. We also model device activities as random variables with a known joint distribution and propose three maximum a posterior probability (MAP) estimation-based device activity methods, which further enhance the accuracies of the corresponding ML estimation-based methods. Optimization techniques and matrix analysis are applied in designing and analyzing these methods. Finally, numerical results show that the proposed statistical device activity detection methods outperform existing state-of-the-art device activity detection methods under frequency-selective Rayleigh fading.