The demand for multimodal sensing systems for robotics is growing due to the increase in robustness, reliability and accuracy offered by these systems. These systems also need to be spatially and temporally co-registered to be effective. In this paper, we propose a targetless and structureless spatiotemporal camera-LiDAR calibration method. Our method combines a closed-form solution with a modified structureless bundle adjustment where the coarse-to-fine approach does not require an initial guess on the spatiotemporal parameters. Also, as 3D features (structure) are calculated from triangulation only, there is no need to have a calibration target or to match 2D features with the 3D point cloud which provides flexibility in the calibration process and sensor configuration. We demonstrate the accuracy and robustness of the proposed method through both simulation and real data experiments using multiple sensor payload configurations mounted to hand-held, aerial and legged robot systems. Also, qualitative results are given in the form of a colorized point cloud visualization.