We perform a critical analysis of the present approach in wave modeling and of the related results. While acknowledging the good quality of the best present forecasts, we point out the limitations that appear when we focus on the corresponding spectra. Apart from the meteorological input, these are traced back to the spectral approach at the base of the present operational models, and the consequent approximations involved in properly modeling the various physical processes at work. Future alternatives are discussed. We then focus our attention on how, given the situation, to deal today with the estimate of the maximum wave heights, both in the long term and for a specific situation. For this, and within the above limits, a more precise evaluation of the wave spectrum is shown to be a mandatory condition.The contemporary, and complementary, theories by Phillips [3] and Miles [4] on wave generation soon followed. On the basis of the Phillips framing of the problem, Hasselmann [5] quantified the interactions and conservative exchange of energy among the spectral components. White-capping, the energy loss by wave crests breaking in deep water, had to wait 17 years after the formulation of the input function before Hasselmann [6], in connection with the JONSWAP (JOint North Sea WAve Project) experiments and report [7], proposed an empirical, but at least quantified and spectrum-dependent, usable expression suitable for practical applications. The adult age of wave modeling was finally reached in 1988 [8] with the reduced Discrete Interaction Approximation (DIA) parameterization [9] of the non-linear interactions, and the consequent formulation of the first third-generation model WAM. The overall situation was well pictured in the so-called WAM book by Komen et al. [10]. Other models followed on the same route: WAVEWATCH [11], SWAN [12], and the one by the Danish Hydraulic Institute.Today we live in a slow evolution of the 1994 situation. Improvements have been made on some aspects of the source functions, computers are faster, and we have gone to progressively higher resolutions. However, although with a rather crude statement, we can say that most of our improvements in the last three decades have been associated with the parallel improvements in the definition and accuracy of the driving wind fields. Indeed, during the last 30 years the only basic conceptual improvement has been the acknowledgement by Janssen [13] of the two-way interaction with the atmosphere, and the consequent need to use a coupled model. Including the interaction with ocean currents, the process is still on its way.