This paper presents some of the research needs to overcome the constraints of different approaches to analyse harmonic instabilities in low voltage (LV) networks. Harmonic instabilities that refer to interactions of the control of power electronic (PE) devices and the network impedance have been observed increasingly in the past due to a growing share of renewable energy generators and other applications that are connected to the LV network via PE devices. Detailed white-box models can be derived if the device parameters are available while measurement-based identification approaches are required to parametrize black-box models. However, both approaches face individual challenges such as the computational effort, restrictions to small signal analysis and unknown system components, e.g. for manufacturers of PE devices the network impedance and for network operators the device specifications. The aim of this study is to present important challenges and constraints of the present methods to analyse harmonic instabilities in LV networks and consequently identify the research needs to overcome these challenges. In addition, measurements are shown to support the argumentation.