Turbulent wakes are ubiquitous in nature and man-made environments. In oceans and the atmosphere, these wakes are generally affected by the presence of stratification. In this talk, I will discuss how the shape of the wake generator influences the course of evolution of turbulent wakes from the perspective of (a) coherent structures and (b) mean/turbulence scalings. In the first part (a), we extract and analyze coherent structures in stratified disk wakes at a moderately high Reynolds number Re = 50,000 and Froude numbers Fr = 2 and 10. The vortex shedding (VS) mechanism is dominant at intermediate distances in both cases, similar to their unstratified counterpart. We use spectral proper orthogonal decomposition (SPOD) to extract these structures. We will discuss how the energy of VS mode evolves with downstream distance, its impact on unsteady internal gravity wave (IGW) generation, and key differences from the unstratified case. In the second part (b), I will present results from the numerical simulations of flow past a prolate 6:1 spheroid at a diameter-based Re = 100,000 and Fr = 2, 10, and unstratified configuration. The non-classical decay rate of the mean defect velocity, observed in the unstratified case, will be discussed. The transition of the unstratified wake to a state of complete self-similarity is investigated by looking for the first time into the far field of a slender-body wake. For the stratified configurations, I will present the ongoing work on the characterization of mean, turbulence, and comparisons with a bluff-body wake (e.g., a disk wake).