The next era of information revolution will rely on aggregating big data from massive numbers of devices that are widely scattered in our environment. Most of these devices are expected to be of low-complexity, low-cost, and limited power supply, which impose stringent constraints on the network operation. In this regard, this paper investigates aerial data aggregation and field estimation from a finite spatial field via an unmanned aerial vehicle (UAV). Instead of fusing, relaying, and routing the data across the wireless nodes to fixed locations access points, a UAV flies over the field and collects the required data for two prominent missions; data aggregation and field estimation. To accomplish these tasks, the field of interest is divided into several subregions over which the UAV hovers to collect samples from the underlying nodes. To this end, we formulate and solve an optimization problem to minimize total hovering and traveling time of each mission. While the former requires the collection of a prescribed average number of samples from the field, the latter ensures for a given field spatial correlation model that the average mean-squared estimation error of the field value is no more than a predetermined threshold at any point. These goals are fulfilled by optimizing the number of subregions, the area of each subregion, the hovering locations, the hovering time at each location, and the trajectory traversed between hovering locations. The proposed formulation is shown to be NP-hard mixed integer problem, and hence, a decoupled heuristic solution is proposed. The results show that there exists an optimal number of subregions that balance the tradeoff between hovering and traveling times such that the total time for collecting the required samples is minimized.