We discuss in a unified manner many existing signals in cosmological and astrophysical data that appear to be in some tension ($2\sigma$ or larger) with the standard $\Lambda$CDM model as defined by the Planck18 parameter values. In addition to the well known tensions ($H_0$ tension, $S_8$ tension and $A_{lens}$ anomaly), there is a wide range of other less discussed less-standard signals at a lower statistical significance level than the $H_0$ tension which may also constitute hints towards new physics. Such signals include, hints for closed universe in the CMB, the cold spot anomaly indicating non-Gaussian fluctuations in the CMB, the hemispherical temperature variance asymmetry and other CMB anomalies, cosmic dipoles challenging the cosmological principle, the Lyman-$\alpha$ forest Baryon Acoustic Oscillation anomaly, the cosmic birefringence in the CMB, the Lithium problem, oscillating force signals in short range gravity experiments. The goal of this presentation is to collectively present the current status of these signals and their level of significance, refer to recent resources where more details can be found for each signal and discuss possible generic theoretical approaches that can collectively explain the non-standard nature of these signals. In many cases the signals presented are controversial and there is currently debate in the literature on the possible systematics origin of some of these signals. However, for completeness we refer to all signals we could identify in the literature referring also to references that dispute their physical origin.