Unconstrained palmprint images have shown great potential for recognition applications due to their lower restrictions regarding hand poses and backgrounds during contactless image acquisition. However, they face two challenges: 1) unclear palm contours and finger-valley points of unconstrained palmprint images make it difficult to locate landmarks to crop the palmprint region of interest (ROI); and 2) large intra-class diversities of unconstrained palmprint images hinder the learning of intra-class-invariant palmprint features. In this paper, we propose to directly extract the complete palmprint region as the ROI (CROI) using the detection-style CenterNet without requiring the detection of any landmarks, and large intra-class diversities may occur. To address this, we further propose a palmprint feature alignment and learning hybrid network (PalmALNet) for unconstrained palmprint recognition. Specifically, we first exploit and align the multi-scale shallow representation of unconstrained palmprint images via deformable convolution and alignment-aware supervision, such that the pixel gaps of the intra-class palmprint CROIs can be minimized in shallow feature space. Then, we develop multiple triple-attention learning modules by integrating spatial, channel, and self-attention operations into convolution to adaptively learn and highlight the latent identity-invariant palmprint information, enhancing the overall discriminative power of the palmprint features. Extensive experimental results on four challenging palmprint databases demonstrate the promising effectiveness of both the proposed PalmALNet and CROI for unconstrained palmprint recognition.