This paper investigates the performance analysis and optimization of movable antenna (MA)-aided wideband communications using orthogonal frequency division multiplexing (OFDM) in frequency-selective fading channels. Unlike narrow-band transmission, where optimal MA positions maximize single-tap channel amplitude, the wideband case requires balancing amplitudes and phases across multiple channel taps to maximize OFDM transmission rate. The authors derive an upper bound on the OFDM achievable rate in closed form for arbitrarily large Tx/Rx regions and develop a parallel greedy ascent (PGA) algorithm to find locally optimal MA positions for OFDM rate maximization under finite-size regions. A simplified PGA algorithm is also proposed to reduce computational complexity. Simulation results show that the proposed PGA algorithms approach the OFDM rate upper bound closely as Tx/Rx region sizes increase and outperform conventional systems with fixed-position antennas (FPAs) under wideband channel conditions. The results demonstrate that MA-aided systems can achieve significant performance gains over FPA systems, especially in scenarios with a small number of clustered delay taps each encompassing many independent paths. The paper also presents a detailed system model, channel model, and optimization algorithms for MA-OFDM systems, showing that MA positioning can significantly enhance channel conditions and communication performance.This paper investigates the performance analysis and optimization of movable antenna (MA)-aided wideband communications using orthogonal frequency division multiplexing (OFDM) in frequency-selective fading channels. Unlike narrow-band transmission, where optimal MA positions maximize single-tap channel amplitude, the wideband case requires balancing amplitudes and phases across multiple channel taps to maximize OFDM transmission rate. The authors derive an upper bound on the OFDM achievable rate in closed form for arbitrarily large Tx/Rx regions and develop a parallel greedy ascent (PGA) algorithm to find locally optimal MA positions for OFDM rate maximization under finite-size regions. A simplified PGA algorithm is also proposed to reduce computational complexity. Simulation results show that the proposed PGA algorithms approach the OFDM rate upper bound closely as Tx/Rx region sizes increase and outperform conventional systems with fixed-position antennas (FPAs) under wideband channel conditions. The results demonstrate that MA-aided systems can achieve significant performance gains over FPA systems, especially in scenarios with a small number of clustered delay taps each encompassing many independent paths. The paper also presents a detailed system model, channel model, and optimization algorithms for MA-OFDM systems, showing that MA positioning can significantly enhance channel conditions and communication performance.